回复：申请 Special handling 劳工卡有关问题

You only need to have an internal posting for filing PERM. Usually your attorney will draft the ad and ask your university to post it as any position posted within campus round. You don't need to post that position again nation wide as the one when you applied for that position.

As long as you took your job within 18 months, you can file the PERM for LC.
If you thing your research and acedamic background is strong, why not try to file EB1b (for outstanding professor and researcher)? You can find my story from my other postings. Good luck.