Thanks for the advice!

Update: We started landing so I just waited until we were on the ground. I tried to check in using my phone but it did nothing except keep giving me a blank page with a Delta home link on it. I went to the SkyClub and they told me that I need to wait an hour and check back for a seat assignment (coach is completely full) but that there are 4 open seats in first, I am definitely on the upgrade list, and am currently number 2. So, things are looking pretty good.