I have a gauntlet lying about I can test this on.
If it is just a spare gauntlet, feel free to test it.
But please don't waste any materials/money on my behalf if you don't have anything to spare.
Make sure you read EVAkura's post as well.
I think that there might be ways to decrease the number of variables working against you, but it does seem like there could be complications.
You might be able to improve your results with the resin by trying to carve out some of the foam. Just make sure that there are enough Polyurethane layers on it so that it will still maintain its structural integrity when you try to remove some of the foam.
Given, if you have a layer that bonds to the foam, then it won't be possible to cleanly remove all the foam, but at least removing some of it should be helpful if one were to try this.
Another thing that might work is if you only resin a section at a time rather than everything all at once. This way, the foam won't be as trapped under the resin and it would allow the chemicals to evaporate as the foam is dissolved. Obviously, making sure you wear a ventilation mask will be important, and it is even more important than when you are just using resin by itself without having chemical reactions and things dissolving.
Now, if you resin it section by section, it could cause some weaknesses in the layer of resin, but once you got through the stage of dissolving the foam, you could come in with some more resin and some fiberglass cloth to make sure everything was nicely reinforced.
As per a rondo stage, where you are filling the internal cavities, I'm not 100% sure on what the best way to play things safe would be, as you obviously wouldn't want it to get on the external surface, but fortunately, as far as I know, it should be fairly easy to sand off if it happens.
Now maybe, there would be a way to add a layer between the foam and the polyurethane that doesn't bond with the foam which would allow for the foam to more easily be removed.
One of my Navy buddies says he has something that he refers to as "resin tape" that he uses on aircrafts that you can bend and shape just by using a heat gun and that it shouldn't bond with or melt the foam, but I don't know much about it.