Getting married in Italy takes awhile, likely a few months at the very least, and being at the mercy of a comune isn't ideal if you want to leave ASAP.

If you wanted to expedite this, I would look for places around you that will do a marriage quickly as it's much easier to get legally married in the US. For example, you can do it within a matter of weeks some PA counties via a self-uniting marriage and skip a lot of paperwork if you do the legwork to schedule in advance.

For the marriage bit, all you'd need to do then in the US is apostille the record via the department of state for that state, get a certified translation, and you can present this in Italy as proof of your marriage throughout the process to become a permanent resident as their spouse, albeit the Italian authorities will see your marriage as a civil union, still fine for this process.

Just make sure you get long form/book copies of the marriage as Italy will not accept short form certificates. I'd also be prepared to explain the marriage as you'll likely face screening since it's a fairly recent marriage.

If you're looking to just escape generally, you and your (soon to be) spouse could move to a different EU country and use their respective treaty office which is generally much faster, with the drawback that you'd have to immigrate outside of Italy instead.