As to your anecdote, how long-term were your tutoring relationships?

Varied, most were in the range of a semester to 2 years.

The post Razib quotes is all about about how everyone fools themselves into thinking that they were much better than the students' previous teachers.

Yeah, this is obviously a problem. I suspect that in many cases I wasn't better than the previous teachers in any substantial fashion, but a 1-1 setting will work better than almost any other setting, so even if the teacher is better at teaching, having a tutor will still likely work well.

One difference between tutoring and school teaching is that some tutoring is for prerequisites that the student now has to use and has motivation to learn and gets a lot of practice on.

This is definitely a problem. A lot of the students I tutored were students who were failing classes because they hadn't mastered basic material from 2 or 3 years ago.

On the other hand, as long as were using anecdotal evidence (which frankly using to this extent makes me uncomfortable) I had one student who was very smart, possibly smarter than I am, and I started tutoring him when he was a junior in highschool and couldn't do almost any math beyond about 7th grade (had trouble solving any equations more complicated than something like x+8=10). In his case it was very clearly an incredibly poor learning environment (although based on other data, it does seem like the the students were so disruptive that the teachers were spending most of their time just trying to control the students). I tutored him for about 1.5 years and he is he's now a computer science major at a respected university, and doing quite well. He got an A in linear algebra two semesters ago and is now taking algorithms and some other similar classes. I obviously had some impact but the fact that his general intelligence was very high obviously helped in terms of success and long-term retention.