File EB1 or EB2_NIW now.
I think your best hope for extension of H1B beyond
the 6-year limit is to file EB1 or EB2_NIW ASAP.
Also continue with your LC. Hopefully, your I-140
will be approved before your H1B expires, so you
can argue that you are qualified for H1B extension beyond the 6-year limit because you cannot file I-485 for AOS due to the visa limit.
Good luck.