Jared, as you know everything about this, I thought I might pick your brains a little...in my own timeline, I have the invention of the cotton gin delayed until the 1830s (there is a good reason for this: someone tried to patent one earlier but was suppressed by Virginian tobacco interests).
In passing, while it's not impossible to delay the invention of the cotton gin by ~40 years, this is a
huge change. The ramifications would be global.
Cotton textiles and mills drove a huge chunk of the industrial revolution, creating booming factories and cities in Britain and New England. Cotton textiles were also a major part of the expansion of the British Empire, allowing them a trade wedge in India and various parts of Africa, and ultimately tying the Empire closer together through economic integration. The textile industry also encouraged further innovation and technological development, too.
The social changes would be noticeable, too. Cotton emerged as the fabric of choice for the middle class, due to its feel and ease of washing (both for clothes and sheets). Cleanliness became a social issue, and perhaps (opinion is divided) a public health issue too.
I'd also be unsure whether the reason you've suggested would delay the cotton gin for so long. There were a whole slew of inventors who were working on equivalents of the cotton gin, due to the huge and obvious benefits of it. British industry was screaming out for more cotton, there was lots of empty land where short-staple cotton could be grown easily. Both wealthy individuals
and governments were keen on anything which would allow cotton expansion.
If all else fails, governments ITTL might end up doing
before the invention of the cotton gin something which they did
after its invention in OTL: offer a substantial prize for a successful invention. Eli Whitney never did make that much money off his cotton gin invention anyway, due to the non-enforceability of the patent, but the Georgian government voted him a very large sum of money as a prize eventually. ITTL, there may well be incentives for state governments to offer prizes instead - cash in the hand is worth more than a non-enforceable patent in the bush.
But anyway, putting aside that rather long-winded tangent, on to the question.
I'm wondering how the South might have looked in the 1830s without the cotton gin.
First and biggest question is how long the international slave trade lasted. In OTL, Britain didn't abolish it until around the same time as the US did (1808), since there was no point doing it earlier. ITTL... well, remember that in OTL about half of all US slaves were brought into the country between the end of the ARW and the abolition of the slave trade in 1808. An earlier or later end to the international slave trade will have massive flow-on implications for the slave population of *North America.
I have the Carolinas still growing a lot of rice (Europe in the 1820s is mad for Chinese stuff as China has been opened to trade, so it fits) and Virginia's main export crop being tobacco, but I was wondering about the other ones you mention.
A second rice boom is possible, although rather geographically constrained in the regions it can be grown. I don't know whether rice could be grown along the southern edges of the Gulf Coast. Maybe. There wasn't much incentive in OTL since sugar and cotton were more profitable, but maybe ITTL it might happen.
Tobacco is still viable, although prices weren't consistent. You may well find that Virginian farmers were still growing wheat (and livestock, too) a bit.
Further west, hemp is still going to be a mainstay in Kentucky. That and wheat are perfectly possible to grow in Missouri, south-eastern Kansas, and for that matter southern Illinois and Indiana. (Whether they will be grown there is a political question, more than an economic one.)
Sugar can only be grown in very limited areas - principally OTL Florida and Louisiana. It would be viable there
provided that cheap sugar wasn't permitted to be imported. (Cheap sugar from the British Caribbean, or Cuba, would weaken the viability of continental NA plantations.)
America, though independent, is still tied to Britain in my TL so indigo might still be sustainable (although Britain is in no position to give subsidies anymore, it would have been until the 1810s).
As soon as the subsidies stop, indigo is probably gone in less than a decade. In OTL, commercial indigo production ceased within about 8 years (from 1792 to 1800, according to Fogel). That was mostly due to the subsidies, although also because Britain turned to Indian indigo. It was also the case that indigo producers elsewhere (French and Guatemalan) could produce more harvests per year, which would further weaken the market.
Interestingly, though, with Britain and America still tied together, there's at least one other industry which may boom: turpentine.
Turpentine, pitch, tar and related products were a major industry in North Carolina during colonial days. Turpentine was almost the petroleum of its day: used in many kinds of manufacturing, as a solvent, an illuminant, and more. Most notably, resin, turpentine etc were a major source of naval stores.
In OTL, Britain drew a lot of its naval stores from colonial North Carolina and related areas. After the ARW, Britain decided (quite sensibly) that it didn't want its naval strength to be dependent on a hostile power, and looked elsewhere. It eventually lifted duties on importation of naval stores from the USA in 1840, and the turpentine industry boomed.
By 1850 in OTL North Carolina alone produced 88% of the USA's naval stores, with South Carolina and Georgia supplying most of the rest, and with major exports to Britain. The turpentine extraction and distillation was conducted almost entirely by slaves.
ITTL, with Britain and America friendly, the naval stores industry is likely to boom sooner.
Also, Europe is industrialising and hungry for cotton to feed its textiles industry, so if a cotton-gin-less South is unable to keep up with demand, what other areas might step up production? Brazil, India?
Nowhere, really, in terms of having the capacity and the cost-effectiveness to do so. Gang labour, the favourable climate and soils of the South, cheap water transport and relative proximity to Europe all gave the South an advantage that nowhere else could really match on that scale. Indian cotton was of inferior quality and too far away, and Brazil didn't have the capacity to expand that quickly. (Or the transport infrastructure, in most regions.)
As per above, you've just knocked a huge chunk out of the Industrial Revolution. There might be a
bit more growth of wool and linen textiles, but nothing to match the massive industrialisation which took place with cotton growth.
Another related, slightly paradoxical point is that while you've just hurt global industrialisation, you've probably boosted
Southern industrialisation. In OTL, from about the 1780s to 1815, Southern planters were investing enough of their profits in industrial and transportation projects that the South was roughly keeping pace with the North in industrialisation, on a per capita basis.
After 1815 in OTL, Southern industrialisation fell behind as more capital was invested in primary cotton production (land, slaves, and ancillary industries). ITTL, with no cotton boom, Southern investment is going to continue in industrial and transportation areas. Northern textile mills aren't going to be around as much, either. While the South lacks some of the natural resources which made the North an industrial superpower, the industrial gap between North and South is going to be a lot smaller.
I also have tropical fruit and peanuts being introduced to the OTL Georgia/Florida area rather earlier than OTL due to different trade ties to a different government in OTL Mexico/Central America. Would slavery be applicable to these crops?
Slavery is perfectly compatible with tropical fruit; it was done a bit in OTL, and could be done more. Without refrigeration, though, I'm not sure how well the fruit could be exported to the key markets - depends on the fruit and the destination.
Peanuts could be grown by slaves, of course - practically any crop could - but I don't know how useful they'd be as a cash crop, or whether slavery would offer any particular advantages.
It'd be worth checking whether peanuts were best harvested by the gang system or the task system (ie workers harvesting as a work gang, or as individuals allocated their own area). If peanuts are best harvested by gang labour, then slavery would be an advantage, as it was with cotton and wheat.
They're just as good at the biting, the Parasite is less optimised for their salivary glands, and the mix of Plasmodium species is different (rather than having all four like in africa, places outside will only have a subset, reducing malarial prevalence).
Interesting. If memory serves, there were also differences between malaria strains even within the Old World. European strains of malaria weren't as readily transmitted by African mosquitoes, and vice versa.