Are you saying that this could not be a Mach3 software problem, that it has to be my electronics?
No I'm not saying either of those.
I can only suggest things based on what you say and when you say it. You have the machine in front of you - I don't so I can only go on what you tell me and when.
Your motors ARE a poor match. However if you say 2 dozen other people have exactly the same system and theirs work fine then despite the motor's shortcomings it may well be that all other things being equal, they are up to the job (though I still suspect it's only just).
Have you set your microsteps as I suggested? Do that first because 16 is pointless anyway so you might as well start with that.
Then I'd suggest you try the following - one by one:
1) find some toolpath that reliably exhibits your problem in air - a few rapids should do it.
2) lower your accel and max velocity by half and repeat. Does it still happen?
3) Because you've just mentioned jogging is ok, try turning your toolpath display off and see if things improve when you run a toolpath that previously stalls.