No one is going to put a gun safe "on a dolly" and run off with it. A gun cabinet, yes, a gun safe, no way. Certainly not one large enough to hold multiple machine guns.
A guy who's going to spend 6 figures on NFA items is certainly going to be spending 5 figures on a safe, I would hope.
Put the safe against the wall, which is where is usually is anyway. Bolt it to the wall and the floor with large, long lag bolts. Obviously, inside the safe.
Between that and an alarm system, which should in itself have movement and opening sensors on the safe, where's it going to go?
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.