Grant Erwin writes:

Is that a workable solution to removing the old tooth from the gold
crown?

No.

Is there a better one?

Melt it out with a propane torch. Improvise a casting crucible by grinding
and compressing bentonite clay (hidden in the grocery store disguised as
the cheapest unscented store-brand kitty litter). Or from silicate furnace
cement.

Gold dealers will give you about half the bullion value of the gold scrap.
They're in it for a profit. Likely no more than $50 or $100 cash for an
old crown, so it may not even be worth the trouble. But you could play
with the jewelry style of metalworking, say casting and finishing a finger
ring.