I have some experience Monokot-ing built up wings and structures, but never had to do a sheeted foam wing. Questions:
1) Is it possible at all? My concern being that the heat intended to shrink the film would melt the foam under the balsa skins.
Yes.
2) If possible, what is the procedure? Specifically, how do you provide for hot air escape? Normally I seal all the way around the edges before shrinking; however in a built-up structure there are plenty of openings for hot gas escape.
Attach at LE and TE, pulling on the diagonal to put on as much tension as you can to stretch it, as you work your way from root to tip. Do not seal the flat surfaces at the root or tip, aside from maybe a tiny tack at about half chord at the root, just to give you something to pull against. When tacked at the LE and TE, go make solid, hot, bond to the LE and TE all the way, nice and solid, and on the bottom, "bury" the edge until the color comes out. There should be no wrinkles, it should already look very good.
Then take a heat gun and shrink it everywhere. Let it cool all the way down - this removes almost all the trapped air that you can. Then, go back over it with a wadded-up T-shirt or some other cotton cloth that is *soft*, smooth, and thick. Heat again with the heat gun, root to tip, and while it's still hot and the adhesive is still hot, lightly rub it down, working from root to tip in about 3" sections. This sticks it down to the wood, and also presses out as much of the air as you can possibly remove. Done correctly, you can see just a slight texture of wood grain, because it is stuck down everywhere. Then, seal the root and the top. NEVER, EVER touch it in the middle of the field with something hard like an iron, or your finger, when it is hot, because it will leave a very obvious mark. I have never managed to use a "sock" on an iron in the middle of the field, it *always* leaves marks where it is stuck down harder in some places than others
Done like this with *fresh* stretchy monokote and kept out of a hot car, it will not wrinkle up later. It will be good enough to get 14-15-16 points at the NATs, if you do everything else right, too.
I would also highly recommend "Tom's Techniques" which was one of the Harry Higley books. It may not agree with above for sheeted surfaces, but I recall not being able to use the "Tom's Techniques" exactly as described in this regard.
Brett