Legal Question in Immigration Law in New York

No one can tell you if the immigration laws will change to take care of people like you.

Marrying a permanent resident doesn't help you for several reasons. If this person could naturalize to US citizenship, that could help without wait (as a five or so year wait applies for spouses of permanent residents) however, you are still amenable to removal from the U.S. without a hearing and such applications for expired visa waiver applicants do pose risks. It may be possible to work for you though. Local policies dictate whether this is wise.

Marrying a common law husband doesn't help in all likelihood. The marriage must be valid at the place it took place at and I'm not aware that NY has such a law, though if you began a common law marriage elsewhere, then there might be a possibility that such could be acceptable in NY. Generally speaking, common law marriage though isn't the basis of immigration status and traditional marriage is recommended to avoid complications.