The V115 that bansuri recommended arrived today.
I’m very impressed, and I’ve already ordered two more! 

There are many YouTube reviews, and this video highlighting the MP3 playback controls really convinced me to try the V115:
The 0-9 keypad allows direct access to any file by track number, as well as access to radio stations by frequency. Moving between MP3 folders could be simpler, but isn’t terrible. One excellent feature is that it picks up an MP3 right where you left off after switching back from radio listening or powering off the device.
The sound is surprisingly good for a small device. Most reviews seem to indicate 6 to 10 hours of listening at a moderate volume. It uses a BL-5C lithium battery, which was common in several cell phone models. They’re cheap and plentiful, so I may spring for a few spares and an external charger.
There’s a sleep timer that can be set for up to 90 minutes in 10 minute increments.
There’s even an undocumented ‘shuffle’ feature. While playing MP3s, pressing the MENU button cycles through repeat one song, repeat all songs, repeat folder, or random. BTW, it shuffles the entire contents of the card, not just the current folder.
One quirk is that it plays the MP3s in the order they were copied to the card. Apparently, this is a common issue among many MP3 players, and seems to be related to the FAT32 file system. The solution is a freeware program called FAT Sorter, and it seems to work perfectly.
After copying MP3s to various folders on the MicroSD card, I simply ran Fat Sorter, selected the MicroSD card, enabled ‘Process subfolders,’ and clicked ‘Sort.’ The files are moved to a temporary folder and then re-moved back to the MicroSD card in alphabetical / numerical order.
As I said, I’m very impressed so far, especially for under $20 shipped from the US. I’ll report back again as I get more familiar with the V115 and its UI and functions.
Thanks again, bansuri! 