Really there should be no path to a green card for H1Bs.. that is against the purpose of that visa. Get an EB3 if you intend to immigrate.
Directly from wikipedia:
"Even though the H-1B visa is a non-immigrant visa, it is one of the few temporary visa categories recognized as dual intent, meaning an H-1B holder can have legal immigration intent (apply for and obtain the green card) while still a holder of the H-1B visa. Effectively, the requirement to maintain a foreign address for this non-immigrant classification was removed in the Immigration Act of 1990."
a) As pointed out by the comment earlier, H1B holders can have dual intent: https://www.uscis.gov/sites/default/files/USCIS/About%20Us/E...
b) Structuring of EB2/3 queues according to the birthplace of the applicant itself is more abusive than most things to do with immigration to the US.