Thanks, hj and Reach4,
I did initially use the hex tool referenced, but the seat was already stripped. I'm guessing someone tried to change it years ago, stripped it and just left it in.
I tried notching a flathead screwdriver into the seat using a hammer (as one person recommended on the net somewhere - thanks for the warning hj!). The screwdriver did notch into the seat and grabbed it fairly well, BUT...I had to use so much force to try to unstick the seat that the screwdriver eventually spun out... I tried this method a handful of times.
I then went to plan C. Went to local big box store, bought some PB Blaster and a screw extractor.
This kit was from Ryobi and the largest screw extractor looked like it might fit the hole properly. Got home, sprayed liberally with PB Blaster and let it sit for a while. I wiped the PB out with a rag then put the screw extractor in and turned counterclockwise with a crescent wrench. The screw extractor seemed to grab the seat to a certain point, but not enough.
I think the problem was that, by the time the extractor was biting into the seat, it was also hitting the back of the valve preventing it from biting in more. If I took a hacksaw, I could probably shorten the extractor (cut the narrower part off) so that the fatter part of the tool would grab the seat without hitting the back of the valve. Or, maybe there is another type/size extractor on the market that would work better.
Any more advice beyond what I have tried?