I put a set of 14x7 Cragar Starwire's with a 3.75" bs on my '65 Skylark, and while it's not lowered (yet), I've scuffed my rear whitewalls on the inner fenders a couple of times when the suspension compresses enough. I do plan on lowering the car at some point, so I'm curious about what people have done to get more room in the rear fender wells.
Seems odd that you would have clearance issues with a tire that small. I have 275/60-15 tires on the back of mine on 15x8" wheels with a 5.5" BS. I also have a `70 rearend under it which is 1/2" wider on each end than the original. Mine are close to both the outer wheelhouse and the frame but they don't rub.
You need wheels with more backspace. For a 7 inch wheel (which measures 8" wide edge-edge), 4-1/2" to 5" backspace should center the tire in the wheelwell. Manufacturers seem to specify backspace based on the outside wheel width, not the tire bead width..... never made sense to me, that's why I prefer the 'offset' spec vs the 'backspace' spec. Some of the early rears were a little narrower, maybe you could change the rear, but measure yours first. I have one from a '64 Olds F85 that is one inch narrower than the rears in my 65-66 GS's. A 64-67 Chevy 12 bolt is also one of the narrow ones. It's possible someone swapped in a later wider rear into your car in the past. You can bend the inner edge of the wheel lip for another 1/2" of clearance. Bend about half of the lips width up. It can be done with a hammer and dolly or with pliers. Bend just a little at a time, go back and forth along the length many times until the lip is bent up 90 degrees. be very, very careful so you don't damage the visible portion of the outside quarter panel.