The point you're overlooking here is that the ability of colonial planters, etc. to influence parliament was drastically curtailed with the Great Reform Act of 1832 which abolished the pocket boroughs they bought and sold and used to influence parliament. It almost certainly isn't a coincidence that the Abolition of Slavery Act was passed barely a year after the Reform Act.
The Reform Act probably helped get a few more abolitionist votes in the House of Commons, but it wasn't the deal-breaker. Discussion of various forms of emancipation had been on the table for years. The key driver for
immediate emancipation was the major slave uprising in Jamaica which started in Christmas in 1831, and which led to a huge upswing in British support for immediate emancipation.
The thing to remember is that the abolition of British slavery was a political deal struck which all sides could live with, both the abolitionists
and the West Indian lobby. Whether the voting power of the Commons swung more to the abolitionists was irrelevant, because Wellington had let it be known that the House of Lords would block any bill which was not acceptable to the West Indian lobby.
So the abolition of slavery bill was worked out in a form, including compensation, which the West Indian lobby could accept. The vote in the Commons was so overwhelming that it passed on a voice vote.
Except that the compensation scheme didn't work that way. You seem to be operating under the assumption that it was an open ended commitment to pay slave owners the market value of their slaves, and the more slaves the greater the amount of money needed. Sorry, not true. The way it worked was that the compensation fund was capped at £20 million, and the way payments were calculated was as follows -
What matters is that the West Indian lobby were happy with the overall deal. They got what they saw as adequate compensation, from a combination of cash payments, receiving the services of the ex-slaves as "apprentices" for six years, and (IIRC) various preferential deals for sugar imports to Britain after emancipation.
Note too that both the size of the compensation fund and the formula for distributing it were set in the Act, before any values for X and Y had been calculated. All that adding more colonies and slaves will do is increase the size of the bath the slave owners take and thereby increase the incentive on them to get their claims for compensation in early before the fund is exhausted.
Yes, it's quite true that the value of compensation was set in the Act, but that value was the amount that the West Indian lobby were happy with (or at least, could live with). Perhaps it may not be quite as high as four times - depending on the details of ATL British North American administration as to whether small slaveholders get left out.
But there are plenty of big planters. If an ATL British Empire is going to free slaves with a Big Sugar lobby and an even larger Big Cotton lobby, then the compensation bill is going to be a lot higher, or it won't be voted through.
Oh and there are a couple of other wrinkles that helped depress the size of the compensation payment further. Firstly, only slaves registered in accordance with the Registry Act of 1819 qualified for a compensation payment. If a plantation owner in rural Georgia buys a dozen or so slaves from his neighbour and never gets around to properly registering them, he's out of luck, sorry.
Someone who owns a dozen or so slaves doesn't really qualify as a cotton plantation owner. The definition of what counts as a "planter" varied, but there were plenty of cotton plantations with a hell of a lot more than a dozen slaves.
Yes, some ATL North American small cotton farmers may have been out of luck. But there would be no shortage of big cotton planters (and rice, sugar and tobacco planters) who would make damn sure that they were eligible for compensation. And that there was enough money to pay them.
And did I mention that the Register is kept in London? Your rural Georgian planter either has to travel to London himself to register the slaves or (probably rather more likely) pay a fancy lawyer in Atlanta a considerable fee to register them on his behalf via a fancy lawyer in London. I suspect many slave owners simply wouldn't bother and would keep their slaves off-register and hence lose out on compensation claims.
Smaller slaveholders may or may not be registered - it depends on how things run in the ATL British Empire. But it's a very safe bet that the big planters would be. And there would be more than enough of them to raise the compensation bill to a much higher value.
And secondly, claims for compensation had to be presented in London. Not such a problem for the major West Indian planters who retained London lawyers and agents, probably slightly more of a problem for our rural Georgian. In fact, this was such a big problem for one group of colonial slave holders - rural farmers in South Africa - that they chose to up sticks and trek into the interior to put themselves (and their slaves) out of reach of the act, with consequences that would be noted at the end of the 19th century. I suspect this might look like an attractive option to some of our rural Georgians too.
The idea of a mass exodus of small slaveholders is an intriguing one in itself, and would be worth exploring if this topic were to be fleshed out into a TL.
But for the purposes of working out whether the compensation bill is going to be higher, it's not really relevant. Big North American planters are what mattered - and there were plenty of those, even if the average plantation size was not as high as West Indian sugar plantations.
As for the idea that the textile trade will provide irrestible pressure in opposition to the abolition of slavery -
Irresistible, no. Strong additional disincentive, yes.
"Since we have discerned, however, that the victory of the free north, in the war which has so sorely distressed us as well as afflicted you, will strike off the fetters of the slave, you have attracted our warm and earnest sympathy. We joyfully honor you, as the President, and the Congress with you, for many decisive steps toward practically exemplifying your belief in the words of your great founders: ‘All men are created free and equal.'" - Petition of the mill workers of Lancashire assembled at the Manchester Free Trade Hall in December 1862 to President Abraham Lincoln.
What mill workers though in 1862 is hardly relevant to what the wealthy landed gentry thought in the mid-1830s. Even if mill workers in 1832 had similar attitudes - which is entirely possible, although I'm not aware of any representative quotes one way or the other - the landed gentry were a whole other story. Even after the Great Reform Act, the landed gentry still dominated the Commons. Their attitudes were not so abolitionist, by any means.