As he says, you should be able to lever the nut onto good thread, or in a worst case lever the entire assembly out of the head - I promise you the power valve is not held in by anything other than friction once you have removed the bolts from the cable carrier (two of them, one shown in your picture)
I've patented the claw hammer technique, so royalties will be due if it works for you, and a complete denial if you break your barrel!
You may be able to get a nut breaker on there, or possibly a dremel to slice it apart. I doubt the shaft is damaged as it is made of very hard metal whereas the nut is relatively soft. Fingers crossed all you'll need is a new nut from Honda...