If you don't want him to have a 10 year ban, DO NOT let him leave the country until he gets his green card. You can file for him while in the US. Because he entered legally, he is eligible to adjust here (assuming he meets the remaining requirements for purposes of adjustment of status). Schedule a consultation with an immigration lawyer.
This answer is for informational purposes only and should not be construed as legal advice.
Get married and sponsor him for LPR status (greencard) He will trigger the 10 year bar if he leaves the US. What you describe in your post re him applying for a visa in Mexico is fraud and a very bad idea.
Due to the nature of this forum, I often do not have all the information required to provide legal advice. Accordingly, my responses on Avvo are intended as general and not legal advice.
Upon marriage all sponsoring paperwork is filed with the USCIS. Generally violations of the immigrant spouse's (when you are married) status are absolved based on bona fide marriage to a U.S. citizen.
Your spouse will receive employment authorization in about 3 months after correctly filing the appropriate petition and applications. He should not travel outside the U.S. even if issued an advance parole document by the USCIS.
Consult with an immigration attorney for case-specific advice. Contact info is in Avvo or at www.ailalawyer.com
Because your fiance last entered the United States with a valid visa, once you marry, your husband may adjust status, and generally his overstay will be forgiven (that is if there are no other pending issues (i.e. illegal reentry while out of status)), and you meet all the other requirements for a bonafide marriage.
This response in no way establishes attorney/client privilege or relationship.
I cannot stress this enough.. DO NOT leave the country. He will incur a 10 year time bar the day he steps out of the country. Your boyfriend entered the US lawfully, thus, upon marriage to a US citizen he can adjust his status to lawful permanent resident in the US as long as you can prove a bonafide marriage. Consult an immigration attorney to help you prepare the correct applications and support documents you will need to submit. Good luck!