Sorry I didn't reply sooner, despite the promise, guys. I was genuinely busy. Now that I have a bit more time before the site is down for maintenance, I'll try to reply to your suggestions and ideas. There's some really good stuff floating around this discussion, as I've grown to expect from AH.com's membership.
There are small tin deposits here and there but the major one was, if I recall, south of there, in Zacatecas down in Mexico. A predominant arsenical bronze is also a possibility in lieu of tin, though one with obvious health negatives which might drive an abbreviated bronze age as the metalworking class starts to look for alternatives which aren't poisonous and still allow them to gain the advantages of strong tools. Might lead to a quicker jump to the iron age. And it's probably easier to find orpiment or realgar than it is to find tin, toxic or not. Apparently there are some minor tin-containing pegmatite deposits around the Lake of the Woods, and some tin available in the Black Hills, but Zacatecas is the only place OTL where we know tin was exploited in the Americas outside of South America.
Hm, bummer. The geography and geology seems sadly limiting.

So, tin would probably be a no-starter and, as you rightly point out, arsenic bronzemaking might not last if people realise the health detriments. One wonders whether a few of the more advanced and organised native cultures could develop enough bronze tools and weapons to discover ironworking by the time they're looking for healthier and less limiting options.
In OTL Old World history, iron seems to have been something of an "equaliser", in terms of weapon and tool production. The effects of developing at least half-decent ironworking and smithing could have a similar huge impact on the societies of the pre-European contact Americas. This is partly why I've also phrased my opening question in the title to include Iron Age era technology.
Bronze-tipped atlatls come to mind as something that could be common (at least at one point) in Bronze America but would not have been common in the Old World.
Interesting idea. How do you imagine one such atlatl, though ? Would it be a wooden atlatl handle with a fairly sturdy bone atlatl head ? And why would most natives waste time making a bronze atlatl, if they can easily make one from wood or antlers ? A bronze atlatl strikes me as being more of a pricy status symbol, perhaps even one sold/crafted purely for decoration and bragging.
Oasisamerica - Mississippian links certainly existed OTL, and if you have as high of a value trade good as tin, then it's all the more important. And how accesible is Black Hills tin? Might make the proto-Pawnee/Mandan/the like cultures along the rivers in the Plains much more important.
There needs to be some reasonable POD that really triggers the peoples of those regions to take an interest in such deposits. You won't get underground mining if surface mining in the area doesn't come first (to at least some extent), and if the surface mining doesn't prove viable, accessible and worthwhile in terms of deposits.
Bronze arrowheads might outcompete them, as it seems an arrow-using culture outcompeted an atlatl-using culture in Montana in the historic era. But bronze wouldn't be used for something as simple as hunting, except maybe for status. Iron, on the other hand...
This is my opinion as well. Hunting arrows will keep using simple traditional materials for arrowheads. Metals will be seen as prestigious stuff, for only the wealthiest members of a warrior society, or some chieftains' most trusted warriors, and so on. It's an especially plausible outcome if the manufacturing of enough bronze for weapons or sturdier tools will prove costly and largely prohibitive, due to overly distant usable sources of ores and other needed materials.
I didn't even know there was tin in the Black Hills. I wonder if there's some kind of publicly accessible GIS of all the world's natural resources.
I'd like to know more about it as well. This is one of those super-specific ATL topics that really requires a person to study all possibilities, even the less apparent and more miniscule ones.
Incan bronze spears / javelins apparently
An Incan copper axe-mace head, you can imagine the same thing cast in bronze for a more comprehensive Incan bronze age
Oh, yeah, I know of these.

I've never seen the star/cog-shaped Incan maces with an added axe head before, though. That's a new one for me ! In an ATL Incan Bronze Age, spears could definitely be a popular choice for bronze blades, even with such blades' infamous bendiness in mind.
For instance, if battles are primarily raids between small numbers of warriors, swords might well serve as the main weapon and can be long given that an individual warrior has enough room about him to maneuver. If battles include larger formations of closely-packed men, spears would better serve as the primary arms, and swords and axes would be sidearms, and thus would be shorter and smaller. You could make five spears or axes with the same amount of bronze you'd need for a couple swords, think of swords as an elite weapon, carried mostly by a warrior-aristocracy, or retainers of the society's elite.
I agree with you that swords would be an elite weapon, especially if native cultures never moved past copper and bronze and onto ironworking. That said, I disagree with your assessment that the sword would be the primary weapon (for those who can afford it) while conducting a raid. Even in the OTL Bronze Age, swords were more of a sidearm than a completely primary weapon. Native American prehistory and early antiquity with an established bronzeworking tradition would still use spears and bows as the primary weapons of war. Clubs and axes would still be very popular, even in one-on-one fights, and particularly if the warriors came from less wealthy social classes. (Ones that couldn't afford even many bronze tools, never mind bronze daggers or swords.) Spears and clubs work perfectly fine in raids on someone's settlement, even a fortified one, bows provide ranged support. What swords could do better than clubs would be thrusting attacks, or slashing attacks, if such hand weapon moves were needed. But spears are better for melee fighting when you want to get up close and if you're content with just bashing someone up, clubs and axes will still suffice.
The kris is actually a very short dagger, and only a few kinds are usable in combat. The one with tens of waves are for ritual and talismanic purposes, the kris which have just two or three curves to them are able to be used in combat, and are still very short, not really a war weapon but rather used for self-defence and martial arts.
Spot on.
I think that the macquahuitl design would be soon abandoned with the development of bronze weaponry. The wooden club embedded with obsidian shards makes sense, but putting in metal blades is less so. For one, compared to an axe or a sword / knife, it will have next to no cutting capacity, being impeded by the wooden club, and can't be used to thrust either.
I think we might see some transitional weaponry that integrates metallic blades into older styles of weapon handles/bodies, but yes, once good enough bronzemaking is figured out, some of the more archaic weapons will be abandoned pretty much entirely. Part of the reason why the macquahuitl existed in OTL was because it was by far the most sword-like weapon Mesoamerican cultures could reliably manufacture with their existing level of (non-metallurgic) technology.
They could converge onto old-world bronze sword designs, but I doubt it'll be too close in form.
For example, these are bronze age Chinese swords
Helladic bronze sword
Near Eastern
All developed the double-edged straight tapering blade design that characterised swords in these regions for centuries even into the iron age, yet all developed distinct designs and techniques in their swordsmithing. What designs of weapons a civilisation produces has much to do with what their martial arts and military doctrines are, which stem from sociopolitical organisation which determine how cultures make and conduct war. Along what independent development, there would also be a lot of cultural exchange in weapons technology and martial arts that would cross-influence adjacent cultures.
I think that bronze weapons in Mesoamerica will necessarily have to take the form of the sword, axe, spear etc. but there is indeed much room for exotic types of blades with unique forms and fighting styles. Just in Indonesia you have dozens of unique and exotic looking swords, like these: And many more.
Part of what I meant already in my original post. Expecting crazy-divergent designs is a bit too much, but so is expecting no differences to existing Old World designs, older or newer. There's enough of a gray area between both of these limits to get creative with the details, but keep the weapons fully practical and usable on a mundane basis.
It's a relatively short weapon, with a a blade a little over 2 feet in length. I would consider it a shortsword in classification, but to be fair, almost all South-East Asian swords that I know of are actually quite short in comparison to European longswords, for instance. But even there, there are swords longer than the average Filipino / Moro kalis, like the kampilan for example.
Yes.
Bear in mind, though, European swords were short for most of sword history. Truly longer swords only appeared in the High and especially Late Middle Ages. The spathas of late antiquity could be fairly long, what with their use in the heavy cavalry, but even those were similar in lenghth to the later Frankish/Viking/Slavic/etc. early medieval sword, or the successor to that, the arming sword. (The typical arming sword was, when taking later longswords into account, a medium sword in terms of lenghth. Katanas and the like were mostly shorter than European longswords, but still a bit longer than any of the roughly medium-lenghth European swords.)
I believe that the reason there's such a huge diversity in Indonesian swords is that civilizationally it was always quite disunited, obviously due in large part to the fact that its an archipelago and different communities always had a degree of separation from each other and even from hegemonic powers. On the other hand, see how similar swords within China are in their preponderance of design (dao, jian etc.), and even see how similar Korean and Japanese swords look. The bottom sword is Korean, and the above two blades are Japanese.
Very good points. Having studied plenty of stuff about the development of bladed weapons on different continents, I can't say I disagree with your quick assessment.
Concerning East Asian blades, there's also the matter that the popular imagination often assigns certain clichés and stereotypes tot hese weapons and the bladed weapon traditions of their countries of origin. For instance, there are quite a few very common Chinese and Japanese sword designs that are, to a layman, quite "European" in appearance. Purely because they're straight, often double-edged, in contrast to the typical stereotype about East Asia having all of its swords curved. (No.) Straight swords from East Asia include the jian you've mentioned, or some of the early samurai swords.
Yes, but don't assume that that cultural diversity will survive the age of bronze or iron weapons, don't forget the Bantu expansion that came with the introduction of iron-working (though agriculture was also involved). In the case of a crop or animal domesticate based POD, it's very likely that due to geographic reasons many Amerindian cultures might evolve into more homogeneous entities, after all, they aren't inhabiting a land of countless disparate islands. Doubtless they'll come into military conflict sooner or later and that'll be one medium for the transfer of military technology.
Yeah, unless we take the Carribean-inhabiting native cultures into account (maybe an Indonesia-like scenario could reoccur there ?), there isn't that much potential for a great degree of insularity. There will be regional uniqueness, but it'll be less insular overall.
Mesoamerica and Oasisamerica would be separate. The Mississippians as well. These are the groups who would most likely innovate on their own considering their cultures. The rest you'll probably need that agricultural POD for.
Possibly.
Although it would be interesting if like in parts of Africa, ironworkers (or even bronzeworkers) end up persecuted for their skills.
Whoa, that happened ?!

I need to learn more about that. Any study/bibliography tips ?
Maybe in some societies, but in the more centralised states the metalsmiths were far too useful to the powers that be, and I expect them to enjoy the favour and protection of the state and the sovereign. Like in the bronze age Near East, smiths who could work iron were kept under jealous guarded lest the secrets of their craft leak out. The more centralised states of Mesoamerica and such would hold metalworkers in quite high regard, I imagine.
This is a fun idea. Definitely helps expand on the speculation of how bronzeworking or ironworking could change the social and economic conventions and written/unwritten rules of the various native societies.