First is that the law of averages tend to catch up to us all. I've had seasons with one flat and others with 6 or 7, seems to average about 1 per 1000 miles over time.
"with really high quality new tires that should NOT allow penetration." Really?? who sold you that bill of goods. Any tire with air can and will go flat given enough effort/exposure. One example we see often are wire bits that weave their way through belted tires, like a sewing needle through cloth, and cause a flat that's usually a slow leak and also one that can be hard to find the object that caused the flat. The same piece of wire if not found will reflat future tubes.
116PSI (are you sure it's not 114psi)? how heavy are you? That's way up there on the pressure range most find relevant. My 150lbs sees 90-95psi for my 25mm tires generally, with no pinch flat issues.
Are you able to figure out what causes your flats? Without this feedback one is shooting in the dark. The location and shape of the tube's hole can say volumes about the cause and thus the cure. Andy