We all been there. My journey to get rid of flats (my tube record: 5 in one ride, hell, 5 in a 1/4 mile stretch !) includes:

1. Wider tires (ie: from 25mm to minimum 28mm)
2. Quality tires (Pirelli, I'm sure there are others, and trash those Conti 5000 tubed creatures)
3. Watch dat pressure - higher pressure for those pesky tubed ones. 75+ lbs for 28mm-30mm
4. TUBELESS for most of my bikes and pressures = 65 lbs for 30mm, 60 lbs for 32mm
5. Did I mention tubeless?

While I never had issues in the old days with Gatorskins, still have 'em hanging on the tire tree (23mm, 25mm, and 28mm), and they do reduce flats, there are many tall tales about their lack of grip in corners and the wet. If I commuted I might set a bike up with 'em though. Bit of a ***** to mount/unmount.