As the original poster, I want to say that the only reason I used USPS was because it was too late in the day friday to have it overnighted. USPS was the only company that delivers on Sunday, so I went with them.
On a positive note, I called my post office at 7:00 am Monday as soon as it opened. They told me that my letter would arrive Monday. I made a comment about having paid to get it there Sunday and that I needed it within an hours, as I had a 9:55 am flight. I was told that I could come pick it up. As the post office was pretty much on the way to the airport, I did that. So, I paid $12.35 for gauranteed Sunday delivery. I then ended up making about 2 hours of phone calls to the USPS and to AA (to upgrade, then downgrade, then upgrade again). As the kicker, I had to pick the letter up a day late at the post office. But, I did get to fly first. The only way I can get a refund for the USPS fee is to head to SFO.