I like the idea of preserving them in a display of some sort, but you can probably come up with something yourself that would preserve them better then a brittle plastic, non-archival slab.
I made up this boxing collage years ago when we moved into our new house. Not for preservation LOL, as it's mostly worthless stuff I cannibalized just to use up a frame and matte I had laying around unused.
It's hanging in my home office, and while it can be argued it's an eyesore
, just about everybody who's seen it has commented on the piece of gum, and likely nothing else in the piece.