I never use any of the adhesive removers on the piece before mirror sliding. if the glue is real dry, it will grab the mirror better. (if you have an oily adhesive remover on it, it will not "grab" the mirror, it will simply slide around leaving the glue in the lace holes.
I release with lace release, if you do this correctly, MOST if not ALL the glue will remain on your scalp and NOT on the piece.....so your clean up job is nearly done already.
DebbieS.