Having continued my search, I found a Photoshop plugin that does the job nicely, even in my ancient version (CS 5.5). Here's the link if anyone else is interested. It's pretty straightforward.
Once you've got the script installed...
- load a series of images into Photoshop using File > Scripts > Load Files into Stack,
- open the Animation window via Window > Animation,
- from the Animation window popup menu, select Make Frames from Layers,
- generate the sheet using File > Scripts > Scriptsheet Generator,
- set the End Frame to the number of layers you have in your animation,
- set the padding if you need/want to, and
- hit that generator button.
This works with either the 64-bit or 32-bit version of Photoshop (if it works with my dino-version, it should work with any version released since then) and might even work with Photoshop Elements, although I haven't checked.
It's also possible you could use it from GIMP using the PSPI plugin from Tor Lillqvist.