I was considering an S-plate, but the method I went with above worked fine!
disassembled the ball top and mounting plate, cut a hole large enough for the the top of the stick's base, put the mounting plate on top, inserted the base from the bottom, and screwed them in place.
Even without actual bolts the stick was top mounted very securely to the panel like this. Pretty good.
I can't think of any other way to top mount this stick to a thick panel properly without cutting a hole too big to bolt it securely.