I just wanted to quickly follow up on this since everything is working now!
Turns out my problem was three fold.
1) As Hijacker mentioned, the main ground from the battery (negative battery terminal to the battery tray) was finicky. It hadn't actually rusted through, as it's still in pretty good condition. BUT, the cable was loose in the clamped metal. It can actually be pulled and pushed around. This really needs to be fixed! Now, it can't be pulled out, as it gets very solid when pulled on, and this is what I've done for the time being.
2) Probably related to combined problems of 1 and 3, but the starter solenoid is bad. Or, rather, very weak. Independent testing shows the solenoid doesn't have the same snap or pull a new one does. Combination of weak spring and aged coils.
3) Starter motor itself is stiff and gunked up. It may or may not have bad brushes (I haven't rebuilt it yet), but the lever is stiff and so is turning the bendex gear by hand. A spare starter solved this issue for me.
So a trifecta of problems resulted in the very erratic behavior.
Thanks your all your help, guys

!