In the OTL the Anglo-Norman descended Cavaliers settled in Barbados and adopted the Spanish Caribbean style of Africa Slavery. When this practice saturated Barbados, the Barbadian Cavaliers expanded to the fledgling colony of Carolina, dominating the Cape Fear region and South Carolina. After the creation of Georgia, the Carolinian Slave Lords attempted to expand their plantation economy south into the Savannah and Altamaha River Drainage Basins, but they were stymied by the fact that Georgia had been founded as a Nonslave colony (and peculiar moral utopian experiment for the "poor" as well). South Carolina eventually won out against the Nonslavery elements and turned much of the south east into defacto colonies for Plantation Slavery.
If you can keep Georgia Nonslave until the Revolution, those alternate Georgians will stay that way. I think if this happens, the Georgia Proprietors will have compromised on some of their eccentric OTL rules. Without those rules Georgia doesn't hemorrhage as many early indentured settlers. With more luck than OTL Georgia had, it's economy will be slightly more focused on light industry and commerce than agriculture. Nonslave Georgians will still want to expand into the Altamaha River Drainage Basin.

Eventually they and South Carolinians will be willing to fight for the the gold in Cherokee lands around Dahlonega in Northern Georgia. Spain might give West Florida away to America at the Peace of Paris in a forlorn attempt to distract Americans from New Orleans - but it seems doubtful.

If Nonslave Georgians could expand into the Apalachicola, and Mobile River Drainage Basin then yeoman and sharecroppers will benefit greatly from the cotton gin, and localized textile processing. Conceivably Nonslave Georgia could extend to the Pearl River Drainage Basin (in the attached map it is described as West Mississippi). Obviously this puts the Trail of Tears back into play.

Such an expansive Nonslave Georgia would be a target for pre-1840s immigration, potentially increasing emigration to the United States instead of just diverting some bound for more northern areas. It would be attractive to German Protestants, and more financially stable North English, Scottish, and Scotch Irish (ironic considering its beginnings). It might even pull in people from the mountains of North Carolina. If Georgia kept its prohibition on slavery, then it would have a very different culture than OTL, probably a mixture between New England, and the Appalachians.
*disclaimer, something looks off with the Tennessee River Drainage Basin in this image, it's like they included part of the Cumberland River and some other fiddly bits. It may be more of a political map instead of an exact drainage basin map. Obviously the Suwannee doesn't take all that is shown in this map, et cetera.
South Carolina would have a big grudge with Nonslave Georgia, and it would only partially be smoothed over in the Revolutionary War. Nonslave Georgia will have a stronger militia than OTL Georgia in the Revolution because it will have a higher population. Nonslave Georgia could conceivably keep St. Augustine in a state of chaos or occupation, it could conceivably repulse the British siege of Savannah, and it could conceivably come to the aid of South Carolina. Nonslave Georgia would not have as big an issue with the fledgling Seminoles in Florida, because it wouldn't care about the runaway slaves down there. Unfortunately, Nonslave Georgia isn't going to be Abolitionist Georgia, any Black people crossing through Nonslave Georgia would be under immediate suspicion, and promptly returned to South Carolina.
Without the OTL influx of South Carolinian slave lords and their corrupt culture I don't think there is going to be a Yazoo Land Scandal, or problems with upstart squatter republics in Georgia's colonial charter panhandle as there was in OTL. Nonslave Georgia would back Roger Sherman's idea of orienting western land sales towards yeomanry rather than speculation.

Of the above watershed based alternate states West Florida, Alabama, and East Mississippi will be easier to keep as Nonslave. The OTL Scotch-Irish adopted slavery where it was in their interest, and opposed slavery where it wasn't - usually regions where they were politically enthralled to English settlers. Kentucky and Tennessee will still become Slave States upon independence.
In this situation, Tennessee might be swayed to manumit its slaves fairly early. If Tennessee can push its yeoman settlers through quick enough, then there is a good chance of Arkansas going Nonslave. In the 1900s, northern Alabama, and western North Carolina could be given over to Tennessee to facilitate hydroelectric and flood control projects.
Kentucky will try to expand its slavery into Ohio, Indiana, Illinois, and Missouri. I don't know how successful they will be, probably less so than OTL. South Carolinians are going to try and send settlers into Louisiana and West Mississippi by boat. I think they will succeed in Louisiana. West Mississippi could be a fairly contentious region. If West Mississippi adopts slavery it would be inclined to expand northwards to OTL Paducah, KY. Mississippi became a state in 1817, and Paducah was incorporated by Kentucky in 1838 so that sort off territorial exchange isn't out of the question. This alternate Louisiana could include West Mississippi, but it could also lack its OTL southwestern bootheel.
This checkerboard potentiality really puts the Texas situation up in the air. I don't know what will happen with East Florida.