See my post above where I documented getting a later checkout at the same hotel when room availability was better.

So the key to getting late checkout may not only be booking on a night where there's more room availability, but also booking the boom that has the most availability. If a room type only has a few rooms, you may be less able to get a late checkout if all of those rooms are booked up for the next night, than if a a room type has oodles of rooms and you're much more likely to get a late checkout because that type of room is not anywhere near booked up for the next night.

Ie, if a room type is booked up for the next night, they have to start cleaning all of those rooms earlier, and cannot give you much of late checkout.

While if a room type is nowhere near booked up for the next night, they are likely to be able put off cleaning some of the rooms until later, and are much more likely to be able to give you a later checkout.

And if that's how it works indeed, then you may have to choose between what's more important to you: late checkout, or a very specific rare room type.

I myself don't have that concern, since I sleep better at around 67F, and smaller regular rooms often have better positioned air conditioners relative to the bed than bigger specialized rooms do. So for that reason I prefer smaller rooms anyway, since I travel by myself almost always.