Sounds like you have several problems going on. If you haven't went through the rear suspension yet stickier tires are going to play hell with worn out 100K/30 year old rear bushings.
275/60 on a 7" is going to roll over and bulge more on the sidewall, 7.5" is the narrow side recommended, I have ran them on a 7" but they fit better on an 8" as they will square up better on the rim.
275/60 on a 7" is going to roll over and bulge more on the sidewall, 7.5" is the narrow side recommended, I have ran them on a 7" but they fit better on an 8" as they will square up better on the rim.