I am using Character Creator 2 and 3DXchange 7.0 Pipeline. For some reason when exporting models to FBX and importing into UE4 all I get are the facial morphs - how do I get the body morphs working as well?

The body morphs cannot exported. You can only use them to create a body that is then exported from CC (intellectual property and all ;) ). The facial morphs are exported though, so your character can speak.

You could export alternate bodies to morph between in UE4.

Wow! You can not export certain morphs.
...learn something everyday.

That's disappointing - Daz will export morphs (it exports BASE morphs and the in-app sliders adjust several base morphs at once). Don't see why intellectual property would play into it if I'm buying export licenses (providing I'm not releasing the source files). The capability would help a lot for game development.