If you marry and petition to adjust your status before your I-94 expires, as long as you don't travel internationally without advance parole, the Sept. 29 expiration would no longer be an issue. If you petition for adjustment of status then leave the U.S. without advance parole, you can expect to be denied reentry on your B1/B2 visa (a non-immigrant visa) due to your declared intention to immigrate. If he's going to naturalize sometime in June, there should be no problem filing before September 29; but if you qualify to adjust your status based on marriage it's possible to petition despite a B1/B2 overstay.
I cannot promise that your petitioning to adjust your status shortly after entering on a tourist visa won't create potential issues, although as I'm sure you've seen from the many forum discussion threads on the issue, people routinely navigate those issues and succeed in adjusting their status.

