I assume if it stopped moving, it would never move again.
Nope, it's a pretty much a one-shot deal (at least in my experience). Get it expanded enough to go on and get it in place before it shrinks. Been there, done that.
Another factor that influences how difficult the assembly will be is the amount of fit interference. The less required, the easier it will be to assemble.
Wes used .004" interference and that's more than enough for this application I'm sure. That he was able to fit four of them with no probems is a great testament to his skill and patience.
Back when I was buiding prototype parts for heavy equipment drivetrains, I've fitted pieces of similar diameter with as much as .025" interference. Now there's some pucker factor!
During assembly, you also have to deal with heat transfer between the hot and cold parts. As soon as the hot band gets into close contact with the cold barrel, the barrel starts to expand. It will set into position long before it actually shrinks to its original size because the diameter of the barrel will increase.
And that is the real point (finally) of this long-winded post. Once it stops moving you aren't dealing with just a band anymore. Heating the band enough to remove it will be difficult because the barrel is going to expand with it. You might be able to get it hot enough that you could drive it back off, but that would be as destructive to the band as cutting (and could damage the barrel). Better just to cut it off and start over.
Like I said: Been there, done that.