Alex! Thank you so much! I would have never thought that the state of edge/face normals played a part in this issue!
I softened edges/normals on the intended mesh in Maya, exported it as an FBX with smoothing groups, and it worked just fine after importing it as a retopo mesh in 3DCoat - Brush smooth, slide edge loops with CTRL, delete edge loops with CTRL, etc all worked.
I also tested it with and without uvs, and it worked either way. The uv set name also did not seem to matter at all either, as my mesh uv set was just named map1. Thank you again!! @Gorbatovsky
John