With that out of the way, here's how I found a private coach out here in the real world.
Ice Girl was taking Learn to Skate lessons at Madison Ice Arena. One of her instructors realized that this was a kid who wanted to be on the ice all the time. Ice Coach offered to coach Ice Girl privately as well. Ice Coach's rate is $34/hour, $17.50/half hour. I said I'd think about it, but Ice Girl had visions of spins dancing in her eyes.
Another LtS level, another offer from a coach. I heard two coaches talking - yes, I eavesdrop! - about how Ice Girl had been putting in tons of time and progressing very far without the aid of a private coach. Well, that got me thinking seriously about the coaching thing.
How did I choose Ice Coach? Well, she's fabulous on the ice and I've seen her teach. She's patient, praises appropriately, and corrects students. Furthermore, it turns out that Ice Coach was a student in one of my freshman English classes 12 years ago (boy, I feel old). If you've ever taught freshmen, you know what I'm talking about here: I know this girl. She was nice, quiet, and shy. A serious kid, but well liked.
Ice Coach also runs the LtS program at another rink, so I knew that she was organized and a member of the USFS.
I really lucked out, I think. Another mom went with a different LtS instructor. What I'm seeing is that the other instructor praises too much and corrects too little. Don't get me wrong; praise is important, but I think that getting the trick/move correct is more important.