If you do go the CarMax / Carvana route, please let’s us know what they offer.
As promised here is where we ended up:
Carvana offered $400 trade-in only, not a cash offer
CarMax initially said "you have to bring it to us, no internet offer", but DM tried a second time (browser navigation is still a mystery to Mom) and she got an offer of $2400. Which she accepted.
She took the car in yesterday to complete the deal. The local dealer is about 10 miles from her home. She promised me that she would only take city streets and not the freeway. I asked her if she had arranged for someone to bring her home and she said she was going to wing-it, which if you knew my mother, is not typical. When she arrived a "nice young man, Jim" helped her and she told him her age and why she was selling the car (played her little old lady card) and asked did they have a shuttle service to take her home. He said they sometimes were able to provide complimentary Lyft rides, and he would ask his manager, which was approved. So that part worked out okay. They did make her wait around for several hours while they prepared the paperwork. She was pretty tired when she got home, having missed her afternoon nap. About 3 hours in total (the time at the dealer, not her nap
).
Before she started asking for offers I searched on Ebay, Craigslist and FB Marketplace to see if there were comparable cars on the market. There are really almost no older Buicks on the used car market around here. I found one 2001 Buick Century, 38K miles in the SF Bay Area, at $8000. This is the same car as Mom's with similar mileage. It's still listed as available for sale and has been up for two weeks now, so the market is not as hot as we believe.
I'm glad to have her off the streets. One less thing for me to worry about. Hopefully her transition from driver to passenger will be okay. Thanks all for your input.