Yes, foam padding would prevent it, unless you like to spend your free time dry-firing your AT. As for the epoxy, I can't see that much stress being put on the adhesive holding the washer to the PT, so you should be fine.
Finally validated on NerfHaven! First off, MIG, great idea and use of a syringe, it's really creative. I have had one of these syringes and was wondering about it's uses for Nerf.
Did you not use the syringe head due to friction issues?
The syringe head (at least in mine) has a very tight fit inside the syringe tube. My guess is it would have friction issues. Also, the head is not screwed onto the "Syringe Rod" and you would need to cut it off, which wouldn't work because I cannot think of an adhesive strong enough to hold the head on.
If you mean just the rubber seal of it, I doubt it would fit onto the plunger head straight, causing seal issues.