It all worked out! Another plumbing happy ending.
I went to Lowe's early this morning to buy the 12" drill bit to blast those nasty plastic nuts off. Since the bit alone was about $8 with tax and I'd never use it again, I decided against it.
When I got home, I called the only plumber that I knew of and they said that they'd be out in about 3 hours and BTW "our minimum is $78". I said OK.
They called me back in 5 minutes and told me that they wouldn't be coming because none of the crews were going to be close to my house and they didn't want to take them off a "profitable job" for a "smaller one". They gave me the name of a local plumber, who I called and he told me he'd be out in a couple of hours.
He showed up early with all of his tools and in 3 minutes (I actually timed hime) her had that faucet off with a plain old basin wrench.
He said, "give me the new faucet and I'll install it for you since I'm going to charge you for an hour's work anyhow".
Long story short, he wasn't in my house more than 45 minutes and charged me $62 - a bargain in my book. Best of all, I didn't have to buy any new tools or spend the day on my back under the sink. I must be getting lazy in my old age /ubbthreads/images/graemlins/smile.gif.
Thanks to all for your suggestions. Except for the 1 suggestion of removing the sink, all were spot on.
Marty