Have a look at your fender gaps, usually when the back 4 mounting points are misaligned it moves the core support as well. Core support bushings bolt to the subframe, before shifting anything you need to look at the body gaps. When you move the frame, you don't want weight on it, support the car at the body. If the front body panel alignment is good, loosen the core support bushing bolts at the frame before moving anything. With the weight off the frame and the bolts loose, it should not be difficult to shift the frame where it needs to be. A round prybar up through the alignment holes should be all it needs.
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