After you bond the edges, give them a few more minutes to fully set up before dealing with the excess fabric. Use a nice, sharp set of scissors for the best results. You'll want to angle your scissors so that one blade is resting on top of the back of the foam, parallel. Trim off the excess fabric, getting as close to the foam as possible without shearing bits of it off.
Continue all around the piece, and nip off any folds of fabric from corners. You should end up with a very neat back edge:
Now flip over your piece, and check that the front is nice and smooth.
Shiny! And it can do this:
Bendy! This stuff can be bent, twisted and crushed to a reasonable degree and will return to its form easily while still staying shiny and smooth. Now, repeat this process for all of your pieces and assemble as you see fit. I personally like building an inner structure out of more foam to attach the pieces to. You -can- bond the surface of the vinyl to the eva foam backing of your pieces, but it is not as strong as bonding foam to backing fabric or foam to foam. To bond the foam to foam, you can use contact cement again, or, since it won't show anyways, hot glue. I don't prefer hot glue in places where it might seep out or warp materials, but in places no one will see anyways, well, it's certainly quicker than the cement.Here you can see the support structure I made for the backpack and all of the associated pieces I have skinned in vinyl. Admittedly, black EVA foam may not have been the best for a photo tutorial.
And here we have all of the pieces assembled together. Weighs about 3 ounces!
Hopefully this will be helpful to folks wanting an inexpensive and flexible option for high gloss armors.