I would try Onshape to import it and send it back to Solidworks as a parasolid file.
I just checked Onshape's website and they accept .3DM
I just had an iges file from a customer that Solidworks botched. One of the surfaces was all out of whack.
So I imported it to Onshape (which was perfect, by the way) and exported it to SW as a parasolid.
Finally, it imported to SW perfectly.
Made me kind of irritated that an expensive CAD package garbled an iges file when a free online service handled it perfectly.
I'd check your Rhino export options as SolidWorks seems to have no options for import of .3dm files. Try exporting in another format such as Parasolid if you can.