The 1/4X20 will probably strip out on the first attempt.
If you want to continue this way, I'd drill and tap a 5/16"hole.
Myself, I use a BIG 3 jaw puller and a 3 pound hammer.
Harbor Freight puller kit with 3 pullers. The big'n hook it up, undo the nut and reinstall it but only 2-3 turns so the...