26.4 diameter tire too big? 68 barracuda

Biggest factory wheel on that car was a 14x5 1/2. Your 14x7 slots are an inch and a half wider, and if they are vintage slots, I'm betting most of that is on the curb side. All of which moves the tire out, and closer to the fender. Which is why you are height limited. Go with the shorter, wider tire.