I realize this is a month old (I did not see if this was solved by a tire change). I just wanted to say I had this same problem on a completely different chassis (1993 Mustang Cobra). It was most noticeable with directional tires - but it turned out to be my solid rear axle was flexing on cracked mounts and following the road imperfections while my front end was tracking straight. It was most noticeable under heavy acceleration.

Obviously completely different application, but could your rear bushing be worn enough to cause a similar effect? If others are having the same issue, it is probably tire related, just thought I could possibly give you one more item to check.

Ryan