Different world. Before one assumes that the middle class will be the same in this timeline as ours, one needs to track the previous 70 years. In the timeline postulated by the TIN, it's just as likely that the colonies will 1) be politically integrated into the British union or 2) a commonwealth excluded from the law. 3) some other outcome.They may not have the power to stop abolition. When the vote was increased to allow the middle class they were very anti slavery and out numbered the rich (who themselves were divided on the issue) as soon as the voting reform of 1832 happened the middle class voted and only took a year to get slavery abolished.
For instance, what if the cotton gin (or any related type invention) is butterflied out of existence, and cotton remains costly and time intensive to de-seed (I know... not likely... the need for the invention was great, so the likelihood of the invention was also great)... but just for the sake of the argument, there is no cotton gin... in that world, the industrial revolution doesn't happen the same way as OTL. The middle class would likely be much smaller. But the economics of slavery would also be far worse.
On the other hand, an American South part of the british colonial system with the cotton gin will further integrate the southern plantation system into the British system. What would that look like?
It's not simply a matter of wishing away slavery. There's the role the colonies would play in the Napoleonic wars, there's the role it would play politically from 1776 until parliament can find a way to pass an abolition act.
I'm not disputing that slavery would last until the 1860s. A South integrated into the British empire (however that might work out) will be influenced by the whole as much as the British system in influenced by the South. I'm saying though, that the cotton production and Southern views will play a role in how and when abolition happens.
The British spent 20 million pounds to emancipate 800,000 slaves in the Caribbean. How much more would they have paid ITTL?