Bead is not being seated properly, which is either a mounting problem (bead not evenly seated), or not inflating properly (using an air compressor instead of a floor pump, which often will lead to uneven seating of the bead). I've used dozens of those CST tires, while not the greatest tire ever made, they work OK. Also check for tube being pinched, must be clear from the tire bead).

"It took 3 of those tubes to realize my bike needed a Schrader valve." If that was done at a bike shop, I would find another shop.

I ran Michelin Elans 100 psi plus for years on my old 1975 Peugeot (hookless Arayas).

+1 700c tubes work fine.