Turns out I was grabbing the file from the top of the qf download page (old version) instead of new version at sourceforge. Well, at least I learned about mesh.faces vs. mesh.tessfaces and how compatibility is broken with each 0.01 release increment of Blender. I will say the changes are well documented.
Anyhow, CTRL-J worked for exporting multiple meshes. For UV, all meshes must be mapped to the same texture. Also I haven't tried animation.
It was great to see the mdl nicely mapped in Quark!
This is not the clearest example, but it's 7 or 8 separate meshes. It's a partially complete player model. Vweps look weird because they're all on at the same time. This is what it looks like in Blender, and then in Quark after export. Only one vwep was selected for export, and it adopted the image from the first mesh. Normally it would be exported separately, anyway.