I went and found a human and asked if it would be possible to get on my original Denver flight and take an earlier flight tomorrow morning. She happily put me back on the Denver flight (with a boarding pass for the Minneapolis flight I was certainly going to miss) but then told me that, since it was now 40 minutes until the flight's original departure time, I could no longer check luggage. My bag is, I discovered, just a bit too wide to pass through security.
So I went back and found another human who indicated that, as expected, she could check my bag after all because the flight wasn't leaving until 6:45, not 4:45. But then I discovered that the earliest Minneapolis flight they were willing to put me on was the same one I would get if I left at 6am tomorrow anyway.
Thus, I have a bonus night in San Francisco. Whee. For added adventure, there was pea-sized hail on I-280 on my drive back to work.