There are many things that you can do too help, but none are going to be a permanent solution. Any 2-part Epoxy will help stiffen it up, I have used Carbon Arrow shafts that I cut down to put inside the tracks and epoxied in and it worked OK.I have heard of people putting steel & aluminum rods, old fishing poles.etc anything that you can cut down and use as the base for the epoxy to set too.
As far as floating out the barrel, take your time and go a little bit at a time with a Dremel. If you take too much off, it will actually hurt it if you do.
Hope this helps-Tim