Does the order that I do it in matter? As in I could do archive invalidation then bash patch? Or vice versa?

It makes absolutely no difference. They are two things are completely unrelated. Use BSA Redirection, through OBMM OR BAIN OR ArchiveInvalidation Invalidated! and be done with archive invalidation.

BSAs and Archive Invalidation - http://tesivpositive.animolious.com/?page=bsas_and_archive_invalidation