So we are making progress!
Received my replacement starter/solenoid assembly from Ebay, and promptly set about removing the old one. It literally smelled like electric death once I got it out (VERY strong odor of the Magic Smoke (TM) that makes all electronics function)
(BTW, thanks to the members here who assisted, or offered to sell me one cheaper than Ebay).
I swapped in the new starter/solenoid, and hooked everything back up. I was able to attach the batteries... without a shower of sparks this time... and ran through some quick diagnostics, following the troubleshooting procedure in the manual.
Once I clicked the switch to start, I was actually able to get it to crank... though it wouldn't start.
And I noticed something else.
Note the diesel fuel leaking from the injector.
I put a paper towel there to soak it up... I assume it needs new seals around the injector? Or would you replace that whole assembly?