245/60/15's on 15X8 rims

On the left side from drum face to the lip is 4 3/4 inches right side is 5 inches.

That's what I was afraid of. That 1/4" came right out of your quarter clearance.

On my '71 Dart I have an 8 3/4 with LBP axles and 11" brakes as well. On the driver's side I also have 5" to the quarter from the wheel mount, and 6" to the springs from the wheel mount (stock spring locations). On the other side I have 5" to the quarter and 6 1/8" to the springs. So, tight side is 11". The LBP axles can typically make use of more backspace than the standard wheels come with, I think Abodyjoe had a set of 15x7's made with 4.5" of backspace for his car...Rear axle upgrade from SBP to BBP

With your car there's two possibilities. The axle is shifted, which means on the side with 4 3/4" to the quarter there's also more room to the spring. Or, it's all in the bodywork. Which means you probably only have 10 3/4" to work with for tires.

If the axle is shifted over you can either fix that, or run more backspace on that wheel. But 4.25" of backspace won't cut it on the side that's tight. If the axle isn't shifted, then you just have 10 3/4" to work with, and that only leave you 9.75" for tire, which is a 245/60/15. Even a 255/60/15 on a 7" rim will be too big.

Some of the 67-69 cars were just tight. I think on the whole the 70+ cars had a little more room, but it's kind of like they ran on the loose side of tolerance and the 67-69 cars ran on the tight side because the chassis is the same.

If you take measurements from your wheel mount to the springs it will tell you if the axle is shifted to one side, or if it's in the quarter lip location.