I tried WD40, Liquid Wrench, & PB Blaster. I also got hold of a torch and tried that. Nothing. I finally just tossed the deck into the back of my truck and went around to some garages. The local car-garage mechanic types didn't want to touch it for fear of the blade. Then, I ran into another guy who also does some of his own lawn mower repairs and he had a set of air tools! So, I took the deck over to his place and we were finally able to break the nuts free and get them off.
I changed the blades and applied some Anti-Seize, but I put the nuts back on manually with the socket wrench.
My thanks to those who responded!