The galley has a copper tube? Can't you just center punch where you want the hole, lay the bit down as close to top of the lifter bore as you can and go to town? Position or angle isn't critical, right? Just need a bit that is long enough to get the chuck out of the way. I've never seen the drilling tool but if I had to make a jig, I'd use some aluminum turned to lifter size with a top stop band. Determine how far down you want the hole to be and drill back from the side to the top so it comes out close to the opposite edge. On small holes like that, the bit will usually get a good bite and start on a steep angle with a decent centerpunch mark.
