As I think about your shorting problem, I really think it might be the stator is grounding somewhere. Your going to have to pull the engine.
Here is how I do it.
Take the grille out
Unbolt the muffler support on the left side (as your looking from the front).
Unplug the headlight if equipped.
Pull hood by spreading it apart off the hinge pins.
Unbolt muffler support bracket from left side, and then all 4 bolts from the hood supports
Pull battery and loosen the 2 fuel tank straps. Pull fuel line off carb and pull tank
Unbolt battery tray and take it out
Take a 1/2" wrench and take the 2 bolts out holding the driveshaft to the flywheel hub.
Take battery cable off starter
Unplug the stator/+ coil plug
Disconnect the throttle and choke cables
Unplug the PTO clutch
Unbolt the 4 bolts holding the engine from the bottom.
I've done this enough on my herd of 140's, I'm sure I can do it in my sleep.
Once engine is on your bench (or what ever you use), pull the shroud.
Take nut off holding flywheel
Using a flywheel puller or harmonic balance puller, bolt to flywheel and tighten the puller bolt. Wack the puller bolt with a big hammer and it should pop. If it doesn't, tighten the puller a little more and try again with hammer. R&R the stator
Engine support stand for working on engine
Pulling the flywheel