Thank you all for the replies.
Here's what we know at this point... Not having seen these but still needing to attempt to get the tractor running tonight we tried putting the battery back to the negative ground setup as the I&T manual indicated. However, this resulted in only a couple of clicks and nothing more. It was dark at that point, so I'm not certain if there was more smoke involved.
A suggestion from my electrician son was to remove power connectors from the battery and run the positive from the battery to the terminal on the starter - if this produced action in the starter, we could focus on there being a short in the wiring between the solenoid and starter or battery and solenoid. This produced no action or sound.
Connecting the negative ground to the starter resulted in a little bit of arc and so we only had that connection for a split-second before stopping.
With no other connections to the starter - no ground, no hot - we used a separate battery and jumper cables in this scenario:
hot to hot (ground to chassis)
neg to neg (pos. ground to chassis)
Neither of these scenarios produced any action or sound. Thinking that the starter might be bad, we decided to remove it only to find that the bendix had kicked out the starter gear and it's now "stuck" in the engine.
I think we need to start over. If I'm understanding correctly, we need to:
1] check all cabling for any bare/broken spots, replace as necessary
2] pos. ground to chassis, neg. to solenoid, solenoid to switch, switch to starter.
Do I have that right?
If the starter is wired backwards from what Allis specifies (wired for pos. power instead of pos. ground), do we have to swap for a different starter or could we reverse the ground on the tractor so that it's a neg. ground with no ill effect?