All you need is enough room to get your hand and a tool in there. I would drill out rivets on the underside. If well practiced, I bet you can have enough rivets drilled out in an hour or two. A picture of the whole thing with approximate position would help.
Practice, practice, practice before drilling on the elevator. Assuming you're dealing with AN426AD3-X, my technique is to center punch on the dimple, start a small hole with a number 45 or 47, then drill with a number 40 down to the bottom of the dimple, snap off head with an appropriately sized pin punch, and then push shank through with same punch. Sometimes, if you're accurate and lucky the #40 drill bit will punch out the rivet.