I'm going to assume your fiance is a US citizen? Your EAD is only valid for the approved employment related to your studies and approved by your school. It's not a blanket authorization to work.
The problem is not one of AOS but reentering into the US on your F-1 when you have clear immigrant intent. They are free to deny you entry on that visa in that situation. You'll need to enter under an appropriate visa (K-1).
Your visa expiry date is less important than your I-94 authorizaiton of stay date an your continued eligibility by being in the program at your school. If you're still legally in the US, you can apply for your AOS without being illegally present while waiting for action. However, leaving the US (as mentioned above) is problematic.
You should contact an immigration attorney before you do ANYTHING. It may be your best move is to get civilly married while still in status and in the US.

