I resolved the wobbling barrel issue by doing mostly that, but I didn't hear clicks. I turned it clockwise only a tiny bit and it was already tight. I've never actually removed the barrel completely, but it's good to hear from guys with more experience that it won't lose zero.
If you fold the handle down all the way you can see it depress the ratchet lock, if you fold it too far down it won't click as you tighten as that disengages the ratchet so you can loosen the nut.
Lock the bolt back and remove the barrel, it's all captured so nothing will fall out. then just slip it back in and with the handle folded down to just before it presses the ratchet thing turn it clockwise, you should hear it clicking until it can't tighten any more then fold the handle back up against the barrel and you're done. It's really easy and it's nice for cleaning the bore and gas system.
If you don't clean the gas system often the regulator gets hard to remove so I pull mine apart every couple hundred rounds.