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Actually, I was streaming when this happened, and it got captured on the VOD:

https://www.twitch.tv/videos/2150126761?t=00h30m05s

(skip to 30:05 if it doesn't do it automatically)

You can see the exact sequence of buttons I clicked to trigger the crash; and then I repeated that same series of commands and it crashed again. (Fortunately, thanks to autosave, I didn't lose my work!)

Oh nice, thank you. Ok certainly because the points have been added before transforming to mesh. I'll have a look, and I see you animated without bones maybe you will find animation easier by using bones, also for mesh deformation it can be really useful : 
https://docs.pixelover.io/tutorials/bones_animation
https://docs.pixelover.io/tutorials/mesh_deformation

For the tail (and the legs maybe ?) you could maybe be interested to use inverse kinematics : 
Inverse kinematics - PixelOver Manual

Genuine question, is there a reason to use bone animation rather than just applying transformation/rotation/skew/etc. to the component images directly (when working with 2D sprites)? I've tried using bones before and while they were all right for more complicated parts of a sprite (legs, in particular), it was an extra step and I'm not sure how much more efficient it makes the process overall.

(Example sprite I made using bone animation, though it really only ended up necessary for the front leg)

I ask because I have to make over a hundred of these animated sprites for my game, so the more efficient I can be about it, the better.

Thanks for linking those tutorials. The inverse kinematics one was pretty brief but that's good info to have on hand. It might be a bit better if it were written out the same way as the other tutorials; or even better than that, a narrated video walkthrough. In general I think PixelOver is a useful tool, but I have a hard time recommending it to my peers due to the relative lack of accessible tutorials. I think if the documentation was more comprehensive / in video format this would go from good to excellent. That's just my two cents; I'll keep on using it regardless.