My suggestion is someone who knows what they are looking at and doing needs to look over all the suspension really good.Still pulls left on lift off. So definitely not wheels/tires.
I was just thinking about this - specifically if there's some kind of toe deflection going on. Your toe links in the rear are basically welded together halves with a nut welded on one side, and a bushing on the other pressed into a welded housing. The bushing at the camber adjustment is better than the stock one pressed into the knuckle at the bottom - it's just a basic rubber bushing that isn't all that strong. Similarly in the front the lateral/tension links have standard bushings as well. If any of those are torn and allowing way too much movement then it might explain the car wanting to move in a particular direction if toe is out only on one side, but ONLY if you're accelerating.Check all the bushings, mounting locations and bolts on the rear subframe. My guess is you have a bad bushing, broken bolt or something to the effect that’s allowing the rear subframe to “walk” under load. It would explain the difference in direction under power versus off power. I don’t think you have a steering issue.
Alignment can be 100% spot on in a neutral setting on the rack, but the moment you’re on the road under load, it wouldn’t matter.
The car really needs to be inspected on a lift without the wheels/tires and with some pry-bars used on different mounting points to see if there’s any abnormal deflection when those spots are pryed on. You could also mount a GoPro or something under the car, different angles to try and visually see where the shift is happening.