The Flaps idea is a good one.
There is one problem with it though.
The Flaps test won't really tell you everything you need to know. As the starter and seloniod isn't under the EXACT same load as when it's in your car with your gear issue. With that exception. it's a good test.
Hell you can hit your starter with jumper cables and your battery and see how it works without a load. (put your foot on it. it likes to rotate)
If'n you didn't have your tranny out already. I would suggest taking your solenoid apart. Cleaning the hell out of it. Lightly lubricate it and throw it back in. Just to see if the gear stick issue would be fixed.
My notion of the gears sticking because of a sticky solenoid is just a guess.
Could also be the starter not having enough umph to spin the motor. That will stick the gears as well. (uneven loading of gear mesh)
Either way... the high torque starter you are borrowing will tell you all that you need to know... (hopefully)
If all else fails.
Hit it with a big hammer......
Claytonious East of Java.