[Cal578]

I did not see anything in the bumper rules prohibiting other materials or parts such as Great Stuff. I wouldn't use it structurally, but using a little to just hold the noodles to the plywood seems like a great idea (it's amazingly sticky). I don't think you'll get any advantage by trying to fill the empty space. In the end, the fabric will really be the main method of holding the noodles to the plywood.

For our prototype bumpers, since the fabric wasn't ready yet, we just used some industrial "Saran wrap" to hold the noodles to the wood. Quick, cheap, easy, works great. That alone is not ready for collision events, but it's good for testing the design. When the fabric covering is installed, we can trim off any exposed plastic, and we'll be good to go.

I saw a couple of teams last year with one-piece bumpers like the OP mentioned, one red and one blue. They worked very well, and changed out faster than most teams using covers. It all depends on your method of fastening the bumpers to the frame. If you have something that is quick-release, you'll be very successful with the separate red and blue bumpers.