OK, it looks like I’ve found a fix/workaround.
In each BulletAppState, I was setting threadingType to PARALLEL. Based on Darkchaos’s suggestion, I was perusing the BulletAppState code, and I realized that perhaps I didn’t need to be doing that. So, I updated my code, and when I ran the game, I found that not only did the ragdolls still work fine, but also that the game no longer crashes after there have been 64. Why that fixes the problem, I don’t know, but, there you go.
As for using a single BulletAppState, I think that might be possible. I’ll look into it tomorrow, and let you know. Even though my problem seems to be fixed, having only one BulletAppState would still be a nicer solution regardless.
Regarding the wiki, I was looking at this page, and the pages it links to. They explain everything, except how to build the DLLs, as far as I can see. This topic gives you some clues as to how to do it, and mentions some things you need to install, but I couldn’t tell what you’re supposed to do next.
So, even though I have solved my problem in a roundabout way, I’m pretty sure there’s still a bug there, even if, in practise, it tends not to affect most people. So, I’ll put it in an issue on GitHub tomorrow.