It doesn't matter how a bullet proof vest is made because it's not suitable for a backstop project. They aren't designed to survive repeated impacts on the same spot. They are designed to stop a bullet once. The bullet gets embedded in the vest - it doesn't bounce off.
I honestly don't know what they do to the Kevlar in a vest but I am positive it isn't a plain piece of woven fabric with nothing to hold it together. It will definately be layered (they look quite thick) and there will definitely be a binding agent of some kind.
Not all resins are rigid. Some are specifically designed to be flexible or semi-flexible. To survive an impact, this is a desirable quality. Usually, the more rigid something is, the more brittle it will be.
The impact resistant resins I have seen are all "semi flexible". This means they can be bent without breaking if enough force is applied but they still feel relatively hard. They are meant to retain dimensional stability but not crack when force is applied. I just ordered some for a difficult mold I am making so it won't crack when I pull the part.
When I made a Kevlar backstop, I added some layers of fiberglass as well as multiple Kevlar layers to give it the flexibility I wanted. It worked fairly well and lasted longer than any wood backstop I have tried but it still had a shelf life.
If I was doing it again, I would use a thick front section of kevlar (7-15 layers) sandwiched in Kevlar and fiberglass reinforced task 12 urethane resin.
Task 12 can be bought from Smooth-on and that is the semi-rigid urethane. It comes as a 2 part liquid like epoxy except urethane usually sets faster. I think that, if reinforced with Kevlar and fiberglass strands that are a minimum of 3" in length, there is a good chance it will survive repeated impacts (for at least a while).
To reduce the noise, I would add a thin layer of thixotropic urethane rubber - painted on the front and back. The front layer of rubber would get ripped to shreds after a while but it's cheap enough and quick-setting enough to re-apply without too much hassle (as long as you don't use too much each time). Unlike silicone, urethane rubber sticks to everything so it won't come off.
It should be a fairly easy concept to test as all the necessary materials are available in small or test quantities.
I would want some fairly heavy weights to hold the backstop down too. A wooden frame or stand would be the weakest link and would definitely splinter or crack after repeated impacts from anything that powerful. A 50fpe 25 cal made mincemeat of some very strong ironwood I tried a while back.
I stuck my kevlar backstop to a brick wall and the repeated impact was not kind to the brick at all. The wife was very mad at me for a week....
If the gun puts out 100 fpe, you want at least 100lb of weight to stop it getting knocked over on every shot. I would put it in front of a strong tree for support..