1998 Virago 1100 - wouldn't idle - now hanging valve?

I've seen a couple of questions about Viragos failing to idle after being left standing for a while.
I have a 1998 Virago 1100 with just 2500 miles on it. It's left standing for several months at a time between rides. I decided to sell it last month - I took it out for a run to make sure it was running OK, then advertised it. A couple of weeks later, I had someone come round to buy it. As I warmed it up, it wouldn't idle. I took it to a local shop, and they diagnosed clogged carbs, and charged me $400 to replace the jets.
So far so bad.

The mechanic then said there was a backfire in the cylinder, and loss of compression.
Then as he started the bike he heard a clanking noise in the cylinder.
His theory is there's a hanging valve, and has estimated $1900-$2800 to fix the problem.

The bike was in near-perfect condition when I put it up for sale, and I had a couple of takers at $3500.

So ... should I pay the shop to fix it and hope to recover some of my money?
Or sell it for spares?
Or take it to a different mechanic?

If the latter, does anyone know of a good Yamaha mechanic in the San Francisco Bay Area?