Today the roof got replaced. I need to take some pictures to post.
It's probably a bit premature to say that this was a good experience, but so far it's a good experience. The workmanship seems to be good and what was really impressive is that they did more than just replace the roof. I knew full well that there were problems in the roof's structure that needed to be fixed - the vents were too low on the roof, there were issues where the water drained onto the wooden fascia board (and rotted it), and there was a leak that was elusive.
All these things were identified and solved. In addition, they brought the flashing around the chimney to current building codes.
My bet is that most roofing companies would have just torn off the roofing and replaced it with new. In this case, problems with the underlying structure were fixed before putting on the new roofing.
It also took one day.
It's supposed to rain in the next few days -- so we'll see how things go when the real test comes.