I wouldn't wet the foam first. If you wet the cloth as you go it's much easier to work any wrinkles out.
As far as bridging gaps it depends on how heavy your cloth is (heavier is stiffer) and how much tension you can get on the cloth. So say you are worried most about the seams on the sides at the top. If you can wrap your cloth around that top corner a good 6" or more, you should be able to sqeegee that cloth pretty tight.
The other thing you can do is use thickened epoxy as a filler for any gaps first and then lay the cloth over it. Apply your filler and sqeegee it flat so there is no excess on the foam. Then lay your cloth right over it before it sets up. Even if you get a low spot you can fill it later because the cloth is supported by the filler underneath.