If I wanted to use a 393 for a purpose other than the VEX competiton, what would be the best way to modify the motor to make it perform better?
I’ve heard that it will burn itself out without the PTC, is there any way to prevent that?
Bypass the PTC so there is no thermal protection. I’ll let you figure out how to do that yourself. 
And yes, if you run it too hard without the PTC you will destroy the motor itself.
No. That is literally the purpose of the PTC.
I would very much prefer not to post how to mod the motors. If you PM me what you want to do with it I might explain a little how to modify them.
If you are reading this thread and know how to mod the motors,
PLEASE DO NOT TELL HOW!!!
Although there are some who would use this for good, this thread would basically be only helping teams cheat. So please, don’t do it.
Honestly, the thing stopping teams from using this method is never going to be the difficulty of bypassing the PTC. Like, there are already threads on this forum saying exactly how to do it, and those threads can easily be found on Google. The only thing stopping teams is (I hope) sportsmanship or (more cynically) a fear of being caught.
That being said, if you’re modifying a motor for a non-competition use but you are also a part of team, be smart and very clearly label the modified motor. You don’t want to use a motor with a bypassed PTC by accident in a competition and then have your mistake get discovered by inspectors.
As for the motors burning out without a PTC, your mileage may vary and consult your doctor before conducting a PTC-dectomy, but we bypassed the PTC on a motor being used for a non-competition project and had no problems. Admittedly we were only running it for a few seconds, but we did go well past the point the PTC would normally trip.
I’ll second this advice, as it’s seemingly very common; most teams that we’ve caught with illegal motors over the past couple of years have stated this as the reason for there being illegal motors on their robot…