Update;
We were in the big city and our destination lead us past Menards so we stopped and picked up a new faucet, just in cast the old one fell apart.
So with the new insurance policy faucet in hand, we put a little more muscle into the water pump pliers.
Sure enough, it came right off with no damage to the faucet.
Then I was looking at a 40 mile round trip to return the new faucet or install it.
We installed it.