Flying with your guns should be simple, especially since you are not taking ammo. Just to make sure you are up to snuff, check both the TSA gun policy AND the airline policy. Airline policy tends to be more restrictive than TSA, but those restrictions primarily relate to ammo, and you don't have that problem. I have flown my guns numerous times, most recently yesterday, and have not had any problems. A few oddities, but no problems.
Having read up on Suarez's classes, 20 mags per gun is probably overkill -- but not by much.
Having been thru other firearms courses, I would take as many as possible, at least a half-dozen per gun. It just makes it easier if you don't have to constantly be loading magazines with ammo.Good luck and have fun, and report back!