I am using the tapered hex tool for removing the faucet seat. I was
able to remove the hot water side, but the cold water side is not
coming off. I am afraid that I might have stripped the hex hole,
because the tool is turning but the seat is not. I have also tried the
standard allen wrenches with the same results.

I was thinking of pounding the hex tool deeper into the hole with a
hammer, but I do not want to destroy the seat. The reason is, the seat
is working ok for now, and the only reason I am replacing is because
it is eating up the stem washers fast.

Any ideas would be appreciated. Perhaps there is a tool out there that
can remove seats with a damaged hole.

Use an extractor with a reverse-threaded taper that will dig in when
you screw out the stripped seat. Tom

use a seat resurfacing tool, it grinds / smooths the existing seat
saves replacing it, under 10 bucks