More in general, call it the high-level equilibrium trap. The society of the South worked very well for the planter elite, to the point where they described it as the beau idea of civilized life. And for getting the iron goods they wanted, getting them cheaply from Pittsburgh, for a notoriously debt ridden elite, is probably better than shelling out the cash to make them locally.
I wouldn't characterise things as a high-level equilibrium trap, just as a scenario where there was limited labour supply and competing demands for that labour. Planters' attitudes to things like industrialisation were very malleable. Even in the greatest of agricultural boom times, there were still slaveowners who were keen to set up factories and other such pursuits. Whenever agricultural prices dropped (which they did, several times), hey presto, most of the slaveowners were prepared to try out industrialisation in greater detail. That had happened before, and would happen again.
More specifically, though, the downturn in iron production had nothing to do with any anti-industry attitudes from planters. It was entirely to do with the economics of the new form of steel production, which was both more price-competitive in itself and also depended on available natural resources (anthracite) which were geographically concentrated. New England, which was the
most industrialised part of the USA, and probably the second-most industrialised in the world after Britain (or maybe behind Belgium),
also had a collapse in iron production.
(Other side of the coin though, Birmingham is nice linked to seaborne transportation. I think for Jared's idea there needs to be a reason, not involving prescience, that has such a group of Southern planters deciding it's worth the short term cost and pain. But that's certainly possible.
The syndicate I described was what existed in OTL. There's no need to invent such a syndicate. What's needed is for them to get enough clout to overcome the small-farmer opposition in the legislature. This should be feasible with a reasonable PoD. (Although, as an aside, this demonstrates that the idea that the planters ran everything in the South was an overstatement. Here was planters being defeated politically by small farmers.)
All that was required was the (relatively) small investment of building a couple of railroads, at the state level. That happened all the time with other railroads. It failed on this occasion, but that doesn't mean it's guaranteed to fail.
While I think that you can postulate some slave-industrialization (they were trying it OTL, after all) the South will still be on the reverse side of a wicked imbalance in miles of rail, industrial capacity, and population that no amount of gallantry and wonderwaffe can wave away.
The odds against the Rebs are long, certainly. All this does is reduce those odds somewhat.
For slave industrialisation, though... without wanting to get this thread off-topic, slaves were widely used in industry. The problem was one of limited slave supplies when faced with a cotton boom (which also stripped slaves out of other agricultural pursuits, incidentally). Whenever cotton prices dropped, industrialisation went up dramatically in the South. And cotton prices were due for a dive in 1860 anyway, due to massive overproduction. (There was about a year's worth of cotton in British warehouses at the outbreak of the ACW). The ACW delayed that cotton price drop for a few years, but as soon as the ACW is over, cotton prices are going through the floor... and suddenly industrialisation looks more attractive again, as happened before.