So, today I found a solution to getting just a bit of oil out of the Triumph: a siphon. Duh.
After precisely measuring out "a bit" of oil, I checked the levels again, found they were OK, and fired it up to let it run a while. So far, there are no new oil puddles underneath. After I take it for a ride tomorrow, I'll know for sure whether or not my repair was a success. I'd take it out tonight but, you know, beer happened.
Tomorrow I'll roll the VX800 outside and try jumping it off the Mustang's battery. I kind of expect it will fire up without too much prodding. But then, I'm kind of an optimist.