Not necessarily of much use to anyone else, but here it is for posterity.
Problem: It is difficult to rewind a short time in my (admittedly cheap) mp3 player.  I need to do this often, since I walk along busy roads, and have kids.
 A note on cheap: It was a gift. It was within my son’s Christmas budget. He now regrets buying it, because I tell them to be less noisy a lot more than I used to.
Solution, Part 1: Split long podcasts into smaller files. It’s easy to go back an entire file. Audacity will do it, with use of Labels and Export Multiple. The Regular Intervals addon is very nice.
Problem: Audacity takes forever. It converts the file into raw data, then back to mp3. Audacity is designed to do a lot of manipulation that works best on raw data, but is not the right tool for this job.
Solution, Part 2: Try several other mp3 splitters. Discover the usual mix of good, bad and indifferent. My first favourite, Splice, also installed several other programs.
Final winner: mp3splt-gtk, which is an open source project on Source Forge. It takes some menu-diving, but it will split the files into equal parts. (The other options are “where I say” and “where there is silence”, as in between songs.) As with many Source Forge projects, it can run on most platforms. (Well, not the -gtk version, but other versions of the project.)
Problem: The files don’t always end up in order on the player. Without proper tags on the tracks, I have to back out two layers of menu to find the next. Most of the programs, including Splice, don’t preserve the tags, at least not in a way my player can display properly.
Solution, Part 3: More menu-diving and experimenting. Use ID3v1 tags, not v2. Also, before splitting the file, edit the tags / properties on the desktop.
There. That works, and that’s how I’ll do it for a while.