Ideas:
1. With the hole saw, drill a hole in a piece of plywood or, even better, hardwood. Position that hole over the existing hole and clamp that down. (that clamping would be the hard part). Then drill from above.
2a. Drill piece of wood with a hole saw. Make the OD of the resulting removed cylinder be a tight-enough fit for the existing hole.
2b. Replace the pilot drill of the hole saw with a rod OR turn the pilot drill around to make the
shank stick out OR use a long "Aircraft Drill Bit" for the pilot,
.
This avoids the pilot drill from milling the hole oblong.
3c. Glue the cylinder into the existing hole, glue the cylinder to the pilot rod/drill, OR support the cylinder from below somehow.