Here's the response I got from Tuff Torq:
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Hello Sir,
Hopefully, with the oil being low in the gear side you did not hurt a thing. Yes, always fill the gear side up to the threads. Also, you could possibly even take the tank off to make sure that the hydro side is indeed full. Please let me know if you have any questions...
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Perhaps it's wishful thinking on my part, but the message I'm reading here is that maxed out fluid on the differential side isn't quite as critical as it is on the hydrostatic side. This would support my earlier reasoning for why the overflow tank dumps into the hydro side of the tranny.
Anyway, I didn't put much time on the tranny (approx 30 min of driving on a flat driveway) with the low fluid, and the time I did put on it was with a fresh batch of 5w50 fluid. So the fluid on the diff side was indeed low, but at least it had good fluid in it, so whatever fluid had made it into the diff side was good stuff.
At this point I'll assume that everything is fine, and will hope for the best. And now I know the proper way to safely and quickly fill the tranny in spite of JD's documentation inconsistencies.