Problem solved. For anybody else facing this, the likely problem is that your rendering is happening so slowly that your FPS is getting messed up.
In my case, I was rendering a high-resolution image sequence. Switching to a video produced animations at the right speed. Reducing the resolution on the images also produced the right speed.
Anybody switching from Unity might expect that all animations in the camera view will slow down to wait for the renderer to draw the whole frame before progressing animations. UE does not do this.
I also tried adding each character to the timeline as an item in the sequence. This allowed me to do a bunch of neat stuff like decide exactly which animation frames would show when. But it didn’t solve this problem.