I was thinking that there is a good chance that Kent might still marry because although the situation in this TL is better than in the OTL, you still have the succession invested in one young woman and her infant son. If the doctors have stated that Charlotte probably won't have anymore children, then the succession is just two deaths away from being thrown into chaos. Charlotte's health may very well have been compromised by the horrid treatment she endured during her pregnancy (the doctors were the epitome of incompetence, really) and then what strength she had was sapped by the birth of her son. Next, you have to consider that infant mortality rates were very high at this time. In OTL, when Charlotte and her baby died, Parliament offered to pay the debts of any of the princes who made real marriages and sired some more legitimate heirs. Again, the situation in this TL is much better than in the OTL because Charlotte and the baby still live, but life is fragile. Parliament may make the same offer to obtain some backup heirs. If Kent is desperate enough (as you said, his debts were mounting), he might just take the offer, and given that he was supposed to have been good friends with Leopold, it stands to reason that Leopold might point him in the direction of his widowed sister, thereby ensuring that there is a good chance that Victoria might still appear in this TL.
This is a good point,
@dcontreras. In the OTL Leopold saw himself as the director of the family fortunes, so it stands to reason that he might see himself as even more so here. He's the Prince/King Consort of England, he's the one who has made the family's fortunes. If he's wanting to keep England in the grip of the Coburg blood, he might very well want his son to marry Victoria. Their subsequent children would be half Coburg, and he'd likely ensure that his grandchildren would be raised in the Coburg way of thinking. Now, I'm not entirely sure how popular Leopold was in England (I know there were many who thought he was nowhere near good enough for the future Queen of England, including George IV), but as you said, Charlotte adored him and their son likely would have been raised to be obedient to his parents (though that doesn't necessarily guarantee that he will be - I'm sure George III and his wife raised their kids to be obedient and look how they turned out). He'd definitely have a lot going for him.