Plaster over latex paint

I'd scratch it up a bit first.

Ask your plasterer. In general they are not keen on plastering overt artex, and latex paint doesn't sound like something you can easily bond to. Another layer of plasterboard is sometimes the safest option.

Depends, and I don't know it. You might have to PVA it to get the plaster to stick, as for a reskim. If the paint is water soluable (like artex), you might find that as it absorbs moisture from the plaster, it comes away from the ceiling (although you can normally get away with plastering over artex itself).

IME plaster sticks well to any sealed surface as long as the first coat is not too thick

No, and you have just discovered why latex paint should never be used on any surface that you don't intend completely rebuilding a few years down the line.

Choices:

2) put up with the uneven, rough-as-a-bear's-arse texture until you move

You /can/ skim over it as it is, but it doesn't stick well to plastic and will crack up and fall off in sheets within a few years