I remember a tenor sax hanging off my neck was enough work let alone having its entire hard case attached :) It seems, to me, the best solution for all of these issues is just to rent a practice space and go play until your cheeks and lips fall off. I am pretty amazed with how the trumpet output sounds through that Yamaha mute, though - it looks like you could even circuit bend that gadget to do some nasty things to a trumpet's tone.