The OP's advice about loosening off the front barrel band a bit is correct.
I ran across this advice in a 1960s Gun Digest.
In my opinion the screw should be backed off just enough to allow you to be able to move the magazine tube with some friction with finger pressure. Too loose might give a bit better accuracy, but then you will probably end up with the screw falling out. You could lock it with some clear nail polish I guess, but I prefer not too.
I also noticed that with Marlin half-magazine guns with a steel fore end cap that the magazine cap screw often applies pressure to the barrel if you tighten it fully.
The magazine and cap are retained by a round post that is dovetailed into the barrel underside. The cap screw threads into that post.
The problem is that the magazine tube may press against the steel fore end cap before the screw is fully tightened, which produces torque that pulls down on the barrel.
The real solution would probably be a small shim washer between the tube and the base of the round post, or to remove steel from the fore end cap where it contacts the magazine tube.
The shim washer seems easiest, I think.
