Is there any way to use a displacement in a propper model? Some properties seem to suggest it, such as the Texture Warp option, but you can't tie a displacement to a propper_model entity, can you?

I personally like to use a old version of propper. There you just create a VMF with all the brushes you want to convert. Everything that is in there will get converted, so no extra entities necessary except a propper_info, or something like that.
I never tried it, but I'm sure it can handle displacements.
And I also think your version can, did you ever tried it?

It compiles propper_models fine, but I can't figure out how to add a displacement to one. I'll download the old version too, and try that. I don't need any inline editing or anything.

I'm pretty sure you can convert displacements to the necessary entities, however the last time I converted meshes was in an old version of propper.