My single handle kitchen faucet leaks worse and worse via the hot side. When I tried to remove the handle so I could tighten or change the washers, the setscrew wouldn't budge and soon stripped the head. I'd like the trick to get that loose, but I bought a new faucet.

Closing the hot cutoff valve didn't stop the leak. I used a strap wrench to make it tighter until I thought the handle would break, but the faucet still leaks. (now up to 4 drops per second, though pressing down on the faucet handle does stop it while I keep pressure on it.)

The cutoff it sweated in and has no external leak. Should I apply heat to the valve to help it close tighter, or is there another trick to this simple mess? Thanks,

Do not apply heat to the hot cutoff, called a stop. You will make it worse not better. There should be a nut on the stem unedr the knob, tighten it with a crescent wrench. Let me know how that works, if it doesn't we need to do a replacement which will involve shutting off your main, they can leak too so keep you fingers crossed.