Mesh Weirdness when replacing control rig skeletal mesh

So coming from the Maya/MotionBuilder world, the control rig seems to be just what I’ve hoped for. However, when I replace the skeletal mesh with my own, there is some weird distortion–the lapels on the character’s coat pop up above his ears and there’s obvious stretching in his midsection (see attached images–same pic, but one has the rig hidden for easier visibility). This character was created in Character Creator 3, and works just fine in general–replacing the mannequin in any sort of run-of-the-mill skeletal actions (I’m mainly building sequences) is fine, it’s only when I try to use the control rig. (It’s even using the same UE4 skeletan as the control rig, so I doubt that’s an issue.) I tried replacing the mannequin with one of Epic’s own characters, and that mesh predictably switched out just fine. What am I doing wrong? Is there something I need to do with the mesh either at import or afterwards to get it control-rig-worthy?

Thanks for any help!