I don't think I quite understand what you mean by twisted the back piece.
In any case, I would remove the zip, back seam, understitching and facing (the relevant party that is) and start again.
For an invisible zip, I would put it in before any of the above processes. So take the two back pieces, insert zip, sew centre back seam below the zip and then think about the shoulder seam and facings. That's the way I would do it. Good luck.