Okay, I found the answer.

Export from MED as FBX 12.x

Then use the older version of the FBX converter from AutoDesk's archives and convert to .obj format, then import into Blender (as an .obj). When I did it this way my meshes and textures imported with no problems. When I used AutoDesk's current version of the FBX converter, my model would import into Blender without any textures (I tried all variations of import/export from MED to Blender too, and nothing else worked).

So thanks!