What is your present tire size? Are you sure you have 14x7's I ask because sometimes rim width is measured incorrectly. Best acid test is the trim ring. If you have the 3" deep rings they're 14x7's.

I now have P235/60R14's (left tire in pic) on my convertible. They're close to stock size height wise, and no issues with rubbing. I was running P225/70R14's (right tire in pic), and I did have some rubbing when changing grades, turning on entry aprons. Oh, my convertible is lowered 2" in front.





For comparison, below is my car with the 235/60's on the passenger side, and the 225/70's on the driver side.









If you have a '67-8 check with those owners on rubbing issues with 14x7 rims. Stock rims for those years was 14x6. '69's have a scosh more room in the tubs to accommodate the 14x7 rims.