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This is a shot in the dark since I don't know if rear caster could cause your issue. I know it can cause bump steer which is a change in the rear toe settings under compression. Does your dealer have the tools to make sure rear caster is measured and set correctly? If not that could be part of the problem. Your description sounds like a thrust angle error but if they have realigned the car several times and the thrust angle is 0 then maybe the rear toe is changing under acceleration due to caster irregularities.
This can be a frustrating conversation since a lot of dealers don't have the tools and a lot of mechanics say there is no rear caster adjustment. However, GM lists it in their Service Manual alignment specs. One of the problems is most mechanics probably read the specs on the alignment machine and don't bother reading the FSM. Since the alignment machine can't measure rear caster they don't know it exists.
You sure it's not the roads? You go drive around in a flat parking lot? The C7Z I'm driving will jerk to the right once in awhile, but most sprots cars with huge sticky tired do as they tramline and follow ruts in the road etc.