@unprincipled peter - sorry for replying a bit late. I'm rather busy at the moment, so I didn't really have time to read through the thread again until now, and since you didn't tag or quote me, I got no notification.
Anyway, I agree with you that things will obviously be different in an ATL. But I also think that people will not suddenly gain new (economic) insight as if by magic. The thing is that both the typical agrarian-minded Jeffersonian and the typical northern Federalist got economics
wrong. And badly so. In OTL, the Federalists and their ideological successors argued for protectionism even when the example of other countries proved that it wasn't working. Basically, even in OTL (with the south within the same internal market), if someone like Henry Clay had gotten his own way entirely, it would have been
disastrous for the international trade position of the USA.
Given the OTL suppport for such ideas regardless, I really think that this...
if the north needs raw materials to industrialize, they are NOT going to tax those raw materials and make home built products too expensive to keep the industries going.
...is too optimistic. Initially, the (presumably) Federalist-dominated north will
not understand or accept that hight tarriffs are a bad idea. Admittedly, they are a worse idea in this ATL than in OTL. So after some time, it will become evident that the tarriffs are huring them. So they'll probably switch to policies like what you outlined. (But I do note that more than reasonable arguments being used, advocates of such a change will be fighting against the deeply-ingrained "tarriffs good!"-doctrine of the Federalists. It's amazing how long people can keep defending failing policies just because they've committed themselves to those policies. Dogmatism isn't just for religions, I'm afraid!)
But okay, let's say they do change those policies after awhile. Good for them. They'll have to make it lucrative for the southerners (who will by then have set up trade relations with Europe, and don't automatically
need the north as an export area), meaning... the south will not be worse off compared to OTL. And once things even out, it gets to be basically the same relation as in OTL. So the north is also no worse off. Nor any better, really.
The fact that they're two different countries does mean: no political fights over slavery (it disappears rather rapidly in the north; it lingers on and on in the south, but doesn't automatically become identity-defining over the course of a vicious regional struggle for polutical dominance). There will be no civil war. Rather, the north will go with Britain on the anti-slavery bandwagon. And if slavery goes on for too long in the south, both Britain and the north will ultimately start to boycott southern cotton (as alternatives, such as from Egypt and India, become available).
Whether a slow death of slavery, exchanged for avoiding the mass carnage of the civil war, is a good thing... I cannot say. But it
is clear that the civil war was highly destructive to the south and its economy. It's not a given, but this alternative might well be better for the south (economically speaking, that is).
All this leads me to believe that in this ATL, the north would certainly not be much better off than in OTL (and the longer thing stick with protectionism, the more likely it becomes they'll be
worse off), while the south might reasonably be in a slightly better position than in OTL. (That is assuming that slavery doesn't end in some kind of rabid apartheid-like pariah state situation. But I honestly think that with the south as a long-independent nation always entirely reliant on export, and without the long history of north-south animosity over slavery, tarriffs, centralism v. states' rights etc. ...the south might be more inclined to start talking about gradual abolition, if the alternative is international economic boycott and thus the collapse of their entire economy.)
I do agree that you are ultimately right that:
the south can very easily be a successful nation, but long term they have to abandon the notion of being a low tariff, little industry country
...but I do think that this change will be gradual, as agrarian wealth in general becomes less of a thing. At that point, the south will become poorer, yes. But it won't be a third wotld shithole by any measure to begin with, and I don't see it really becoming one. And that was where we initially seemed to disagree. My contention was and is that the south will not "
remain a third world country" (because up until the mid- to late-19th century, it's actually going to be
very rich). At worst, it fails to organically adapt in the late nineteenth and early twentieth century, and will thus see its (rather vast!) agrarian-based wealth slowly melt away as it gets left behind by the modern world.
If they're smart, they start industrialising once slavery is ultimately dealt with. The great internal wealth disparity would allow the south to set up competitive industry based on their cheap labour, even if they are late to the game. If they do this, things will even out. (As their wealth increases, wages will go up, and the south will become... well, a regular, industrialised country.)
If they're not smart, they get to be relatively poor for several decades (I wouldn't say third world, but definitely a backwater), until folks up north get the smart idea that wages up north are high, while those down south are lower. At which point northern industrialists will move their factories down south, because that's cheaper. Which will actually boost the southern economy again, creating new jobs and wealth, which would gradually drive wages up, etc. ...while creating a rust belt up north.
(At which point a northern president with an exceedingly silly haircut will get elected by promising to bring back the high tarriffs of old. And to build a wall along the Mason-Dixon line.
And the south will pay for it! 
)