Older Electric Windshield Washer Pump Repair ("Rebuild"?)

You went much further than I've had to do. I've pulled the cover on dozens of those pumps to free them up. It's almost always the plastic pump section that locks up. I just run some WD40 or similar into the pump inlet tube and grab the input shaft of the pump section with some needle nose pliers to work the shaft back and forth until it frees up. It's usually just some water deposits/rust that locks the gears up. Once you break them loose, the motor will now spin them. Stick the cover back on and you're done. Just take care with bending the aluminum lock tabs on the cover. The will break off easily if you get carried away or rebend them more than a couple of times. I bend them just enough to get the cover off....no more.