Updates:
1) Finally noticed that the reason the gearbox was seizing wasn't the G&P M120 motor but the metal bearing spring guide not allowing the stock spring to compress enough to allow the piston to move all the way back. It reduced the travel path of the piston by a couple mm and it seemed to be enough to stop the cycling in its tracks fairly often (but thankfully not blow anything up). Went back to the stock spring guide and the problem went away.
2) Tested the above update until I was satisfied things were stable. Wanting to toy around with compression and power, I replaced the stock spring, which fires about 360fps, with a new spring, a Modify S110+. The stock spring is one of the ones that attaches to the piston head, so I replaced the piston with it. I tossed in a spare Madbull X-Factor piston I had lying around (picture below), and the finger-over-the-nozzle compression test yielded some encouraging results. I chronoed the gun, and it now fires about 400fps. Hopefully the hopup bucking keeps up with the faster velocities.
3) Having convinced myself that the upgrade motor I originally got for this gun probably doesn't have any gremlins in it, I re-attempted to update the motor from the stock JG motor to a G&P M120 short type motor. This motor's pinion shaft isn't as long as the JG's, so it requires quite a bit of motor height adjustment. Unfortunately, the motor cage on this AEG is made of a very soft metal, so the entire cage actually bends its shape slightly if you apply motor height. This means that the motor adjustment screw and the motor cage screw at the bottom of the pistol grip do not align with the pistol grip's bottom! I had to unbend it a bit and complete the height adjustment with the gearbox placed in the lower receiver. A new gearbox and motor cage might be on my list in the future, pending some research.
At the moment though, it runs great.
Here's a video comparing the motor RoFs on a half-discharged 7.4V 800mAh LiPo:
JG G36 Motor Upgrade - YouTube
I'm still really pleased with this rifle and hope to keep nudging its specs upwards as I experiment with various upgrades. I'd like to gradually turn it into a monster as I learn things.