Instead of fabricating a cup, I fabricated brackets out of steel and bolts that essentially make the jack a part of the airplane.
One end screws into the bottom of the plane, in the tie down hole. The other bolts to the piston on the jack. We tested it tonight, and it works as intended.
I might still grind a little "divot" in the top of the piston, just so the bracket can't move at all, but so far that seems unnecessary.
Here is a tongue-in-cheek pic taken of me with my "gorilla-engineered" bracket (alcohol may have been involved):
And here is the jack, in action, this evening. It's stout as a bridge.
