Change the rim tape (of course it kinda depends on where the tubes are
opening up - which you will only figure out by dismantling them
yourself) Take the tire off, run your fingers around on the inside of
it and see if something bites you. If you don't draw blood do the same
with the rim. Maybe it's worth $50 bucks not to get a little tiny
piece of wire poked into the tip of your finger.

You sound like you might be the guy they make those air impregnated
foam tires for, google greentyre. I don't mean this to sound like a
dis... just an idea about practicality of your circumstance. These
things sacrifice a little bit of performance for a lot of reduced
maintenance. If you're riding knobby tires on pavement and hard
packed surfaces performance probably isn't one of your primary
concerns anyway.