Had very similar symptoms on my XLR when braking to a stop and starting from a stop. It was a very slight bump that grew more pronounced and annoying over time.
The seats move forward and back on long worm drives located on each side of the seat. The forward/reverse motor spins the worm drives and a threaded adapter on each side of the seat frame travels along the drive to position the seat. Each adapter had a pair of rubber bushings (shaped like washers) that acted as cushioned hard stops to dampen the movement when the seat reached its end of travel. Over time, the rubber wore and the spacing grew, allowing more play within the adapters. This may be what's causing your problem.
To fix it, I removed the slack around the worn rubber bushings by installing modified (one outer edge sanded down to match the adapter profile) thicker nylon washers in the adapter after removing the worm drives from the seat. The fix cost less than a dollar, but it took a couple of hours to remove the driver's seat, mark the worm drive rails with blue painter's tape prior to disassembly, (to ensure each side was aligned with the other when everything was re-attached to the seat frame) and replaced the worn parts with modified washers.
Car seats are very heavy and bulky, requiring thick padding laid down over the rocker panels to prevent scratching during the removal / re-installation process. The fuse needed to be removed from the airbag system prior to removing the seat to avoid inadvertently triggering the airbags as the seat was removed.
The only way to know for sure is to remove the seat, flip it over and look for any signs of wear or excess play where the adapters rest on the work drives. if one side is worn, it could cause the seat to skew slightly under load during a turn causing the shift you describe.
I've attached a couple of pics to help clarify my description. I used them for a repair procedure I placed online for the XLR community - this turned out to be a common problem with the XLR (and Corvettes) as they inevitable age. Hopefully, they might be of help to you - or anyone you find to troubleshoot the problem.
Before you get too involved with this, I recommend checking the tightness of the seat floor pan fasteners; there are two at the rear of the seat. The front of the seats have tabs that fit into slots - this may allow a small amount of play as well. If pulling the seat, remove the rear fasteners, then lift the seat up and back to disengage it from the slots.