Cool idea, you should try it so we have real photos of how it looks. I've tried welding plastic before, it's a PITA and the results have been marginal at best. However, I've stuck plastics together easily, quickly, and permanently with this stuff:
I'd buy a set of the both the orange and clears so you've got new pieces to work with. If you do a nice, clean cut you could possibly join the pieces at the ends and make it look stock. Go for it and take photos!