I want to take a cubic environment map that was shot as top, bottom, and four side panels and convert that to the more conventional panoramic style.

Does anyone know of an app, a plugin, or a process to do that?

I think from this post Environmental Shader - used in 'Chicor... you could use Dusan's project (with a little modification ) to use your images. He already distorted the mesh and set up the camera to render the panaramic image.

Or yo could try creating the mesh distortions from this Cubit to Cylindrical conversion

I seem to remember that there was a program called Pano-tools that did conversion, can't find it on my drive at the moment, but I'm in the process of cleaning up right now, so who knows.

If I remember correctly, the free HDR Shop v.1 can do that

Yup, HDR Shop can do it. I managed to get it to work under Darwine for those mac users out there.

Photoman