Im ambi- so sometimes I carry "strong side" sometimes the other, depending on what Im doing, other times I carry cross-draw,also depending on what Im doing.
I train myself as equally as I can in all 3 modes for OC and CC.
From cross-draw I even try to practice Cavalry draw with the left hand, to account for the possibility of the "right/strong" hand being in some way injured or disabled or otherwise occupied.
As for actual shooting, I alternate holds when shooting as well. 1 mag strong hand, 1 mag "weak" hand,1 mag both-hands, etc.
My own feeling on the matter is if I limit myself to only one method of carry/draw/shoot, I limit my options, and invite Murhpy too openly.