I may be able to help a little here. I've designed a few high-stress parts that required parts to be shrink-fitted.
In this situation, the large diameters of the tube and bands are a definite plus, but we'll get back to that later.
First of all, most people go way overboard on the shrinkage. It's surprising just how little interference it takes to securely lock two pieces together. Excess shrinkage does not add security, it only imparts stresses on both the band and the tube.
When planning the fit, consider the minimum interference fit that will keep the piece secured against the forces attempting to move it. In this case it's just the recoil and that isn't going to move a band with a good, clean interference fit of as little as .005". I would consider .010" the absolute MAXIMUM for this application.
Expansion is greatly influenced by circumference. That's where the large diameter of these pieces is a plus. For the same desired expansion, a band with a large circumference will 'grow' in diameter with much less heat applied than one with a small circumference.
In the case of these bands, the concerns about heat altering the metallurgy of the tube are pretty much a non-issue. It won't be necessary to get the bands that hot. Significant expansion occurs well before the steel gets red hot, Afterward expansion slows to the point that it takes a LOT of heat to make it continue to expand once it's glowing red.
Only parts assemble under very controlled conditions can be heated to this level and recovered intact. I've done it with very heavy fits (.025"-.030" @ 5" diameter), but it isn't easy.
So that's my contribution to this discussion. Take away from it what you will.