I agree about the flex. I have observed this too, but on my gun it does not seem to be as pronounced as you have described yours. Nevertheless, I have never liked how the barrel does not thread all the way. It really should lock into place when threaded all the way. I currently use YELLOW Teflon tape on the outer barrel's threads. Yellow tape is thicker than white and works well in this application. It helps quite a bit.
I have been considering one of these two things as a solution:
1. Find some sort of big, thin spacer/washer that I can use at the barrel-to-receiver connection. I thought that I maybe could get it so that the barrel screwed in tight against the washer, making the whole thing more solid.
2. However, the idea I like even better is to VERY CAREFULLY shorten the outer barrel by maybe 1 thread. I would probably use a hand file (bastard file) to remove a little metal at a time until I could screw the barrel all the way in until it seated tightly with the set screw aligned.
Shortening the outer barrel would move the inner barrel and hop-up assembly closer to the cylinder, and it is possible that the cylinder head's nozzle might have to be modified to accommodate this. But seriously, I imagine that if you are competent enough to correctly bring in the outer barrel, reworking the cylinder head should not be any more difficult.
Peace and grease