Handle removal difficulty

Diverter handle, 2 valve type. Puller keeps slipping off; the bezel behind it has a large diameter & the "L" shaped meta hookl keeps slipping away.

Drilled it out, 1/8" drill, 6" deep and still stuck.

Next step a torch.

Isn't there a better type of handle puller tool?

Been on there AFAIK since circa 1966... scum, or maybe originally forced & swaged on ???

Some handle pullers are just too lightweight for the more challenging jobs. You may be able to put a clamp of some sort
on the puller arms to keep them in place.