to prepare yrself for applying PERM while fighting

your H1-B transfer being approved does not have any relation with your I-140 immigration visa petition

If your new company does not fully take the legal responsibility of your old company and/or did not amend your pending LC after acquisition, it might be an excuse for CIS ...
Anyway, you may consult a good immigation lawyer to thoroughly analysis your case and then decide the next step

BTW, I do think it's a wise choice to apply PERM in case of this pending appeal turnning out to be declined eventually