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

Any special prep of the wood?  Sanding?  What grit?

i have a slightly different method for monokoting. this F3a plane have wings and stab fully sheeted foam surfaces and all monokote covering.
sand everything with 500 grit sandpaper, then use high pressure air spray over the surface to clean up the balsa grain. this will raise some "hair" from the wood, i run my hand over the entire surface to get rid of the raised spots. do not sand again.
I seal the edges and let a small air escape unsealed like 1" segment and use the heat gun. when air is off, i end sealing and let the covering "floating" over the wood, never seal over the sheeted surface to void showing the grain or wood beneath. looks like a metal surface highly polished. Pros: looks like a perfect paint job. cons: may develop some slack but you always can stretch back with heat gun.

Mike,
I covered non protected blue foam wing with Monocote using minimal heat. Work from center to tips and edges. Low heat did not make any air bubbles. I covered with Monocote the black foamboard wing (paper covered foam) in the same way. If seal TE and LE overlapping top and bottom covering as was mentioned earlier, then wing will look smoother. But covering will not strengthen the structure. Balsa sheeted foam wing preparation- sand with 400-600 grit, blow with compressed air, wipe with tackle cloth. Any glue joints, any saturations with superglue or reinforcement with fiberglass will be highlighted after Monocote or ultracote covering.

If use ultracote it can be scuffed with scotchbrite and steel wool and be painted over. Hangar 9 ARF Blue nose P-51 is covered with ultracote. Covering is painted in matte silver, added panel lines, rivets, hatches. Than the ready sheet is applied on the airframe. They even sold rolls of prepared this way ultracote separately.

Jerry

It takes *extreme care* to avoid even the slightest mistake and painting is generally much more forgiving - if you screw up paint, you can always go back and fix it.
   
    Brett

Especially if you don't apply the film taught in the first place, and end up pushing a wrinkle into the film as you push with the cloth. If you pinch a little wrinkle together, it's permanent!

Mike,
Ultracote has one good feature. It’s resealable. If you don’t like result of covering with it, you just heat up the area with heat gun , peel the material, reposition it, and seal with iron again. Or peel all of the “cheap“ mono/ultracote covering and cover the wing with silkspan. 
Last year I started Monocote covering my Ringmaser parts on Oct. 4, 2019 at 4 PM. And I finished Covering, gluing tail, soldering control rod, and final assembly and settings electronics on Oct.5, 2019 at 7 AM. All it took 15 hours. With silkspan and dope it will never be that fast.

Ringmaster’s solid balsa fuselage I covered in Monocote using low heat. Working from center to outside, no air bubbles . After all fuse was covered, I used heat gun to melt/ adhere adhesive. While area was hot ( reasonable) I used folded bounty paper towel wet with isopropyl alcohol to gently rub Monocote down to adhere to balsa and cool it in the same time. Heat can be regulated by distancing from surface.

Jerry

Dane,
I was in rush to participate to fly in Syracuse Ringmaster event on Oct.5, 2019)) On the fifth flight I crashed it because I did not have enough sleep.

Jerry

I've done one of those every year also. Lol