Actually most cell phones show the voice mail messages as the time they were picked up from the tower...I have AT&T and it ALWAYS shows the time I turn the phone on and it gets the messages. My messages don't get time stamped at the time they are left.
I'd just go in and talk to the chief pilot face to face. Explain to him what happened. Say you're very sorry, you feel like a complete idiot, you can't believe it happened, it'll never happen again...and you don't want an MA on your record and you'll do whatever you can to get it removed.
I can't speak for your chief pilot, but some of the guys I've met that are CPs at Eagle would remove it or work with you to get it removed. MAs are not set in stone...believe me.