I used to use Specialized Turbo Armadillos..... they don't make them anymore. I have not used their newer ones. The only time I got a flat was when the tire was when I wore the rear down well below where it should have been replaced. They had a poor lifespan though, I had some saved..... but they all went brittle on me in storage, despite no light.

No tire is flat proof though.

How old are these Michelin Axial Super Comps though? I don't think they've been made for years, have they? Some tires loose their integrity over time..... then you'll get lots of flats.

Schwalbe seems to be a hot brand right now, but some of their tires cost more than a car tire. A bit overpriced.