WI Venice casts an eye Westward?
Wait a minute. In all the timelines proposed in all the years of the AH site, doesn't anyone wonder WI the Venetians cover their bets of holding trade to the East--by going West too?
Specifically--get control of Gibraltar and whatever point of land on the south side of the Strait is best for a seapower to hold--would that be Tangier?
This is in aid of Venetian traders seeking trade links to Northwest Europe--England, France, the Low Countries.
In the course of doing this--this is a side venture from their point of view after all, their efforts are still mainly as OTL on securing the Eastern trade--they eventually do a little exploring down the African coast, find one or more of the sets of obscure Atlantic islands--Canaries, Madeira, Azores--perhaps pick up on rumors of lands to the West from Northern Europeans....
The point being, either they preempt Portugal, Spain, or both, or at any rate are in a position to cut themselves in on the America trade when some European rediscovers America and makes it stick.
"Venezuela" might be literally a "New Venice" then?
What I'm suggesting has a whole range of possibilities, from ASB VeniceWank (they just don't have the population base to replace Spain after all) to a mere marginal survival where Venice is just barely hanging on there in the modern day.
In fact if Venice is not remarkably strong and the whole map of the Mediterranean is completely redrawn by 1800, I can only see Napoleon abolishing the place. Then it might get restored in the post-Napoleonic settlements, and then eaten up again during Italian Unification, by the HRE, post-WWI, Hitler would surely either eat it or feed it to Mussolini, etc. At some point Venice surely gets absorbed into some larger entity, unless it is such a large entity even as the 18th century ends that its national ID cannot be ignored.
Another way to go is to have the home republic eventually perish completely as an independent power, but have a former colony, cut loose by that event, continue an independent career.
Aside from American territory, what about Venetian South Iberia/North Morocco--basically Greater Gibraltar? They start with securing control of the straits for narrowly commercial purposes, but holding on to the basic claim doggedly, naturally the territory they control tends to grow, to give more depth to their holdings and to give it enough of an economic base to be self-supporting. By the 18th Century, Britain might ally with this cadet branch of Venice (with or without allying with the mother city, depending on how that relationship has evolved by then) rather than seek to hold Gibraltar herself.
Either that, or "Britannia Rules the Waves" gets butterflied away completely--as they'd fail to get anywhere in the Med unless the Straits Venetians let them.
Ah well, for Gibraltar to be a possession worth having, one either needs a larger empire it is a vital point for, or to somehow profit from the trade of other powers passing through.
I'm just throwing out concepts that lie westward, rather than throwing in the towel and saying "Poor Venice is doomed once someone looks West..."
Mind, I'd agree that these are less probable timelines, because the Venetians enjoyed great success for a time in reaching Eastward, it probably would not occur to them to cover bets to the west, especially as that would divide their efforts; unless the Western colonies could pay their own way they'd look like a pointless diversion, and even if they were rather profitable it would still represent a drain of total manpower. Unless somehow this diversion gives them a new pool of loyal talent to draw from, either in Western territories themselves or by reconfiguring their efforts in the East so as to make recruitment of allies there more probable. Suppose the Venetians could make themselves less hated among Greeks for instance, and wind up with the loyal help of at least certain Greek peoples--then they'd have more manpower to reinforce both their Eastern operations and Western ventures.
At the end of the day I'd agree with this much:
Either Venice grows to be a much greater power, conquering her own region as a distinct national realm on a modern nation-state scale, and/or having a colonial empire of some territorial significance to draw from that is more or less defensible in the context of the 17th, 18th, 19th, and 20th century snakepits;
Or at some point Venice's time has past, she can't hold on to the sorts of mercantile trading post colonies and systems of extorted concessions that worked ok in the early part of the second millennium but not so well as the scale of things picked up. Once eclipsed, Venice does not last, not as a power other powers seriously reckon with though it might be convenient for some major power to keep it in play as a nominally independent state. Eventually absorption into larger Italy (or some other state that pre-empts greater Italy, such as a stronger HRE) seems inevitable.
This sad fate could easily overtake her even if there were a whole string of Venetian trading posts down the African coast and major concessions in the ports of NW Europe too; at some point Venice needs to develop a possession that gives her a major population center somewhere--either by acquiring a lot of territory in the neighborhood of the home city, or founding a loyal overseas colony that the mother city can rely on to hold its own and also rally to her aid, or at any rate carry on the torch of specifically Venetian identity when the tie is at last severed.