Hi Doug, that work flow is not what Composer is meant for. You should be going from SolidWorks to eDrawings, not Composer to Edrawings. Composer is a graphics program, not a CAD program. I try to think of it as a one way street for the CAD portion. Once it is in Composer, then you can export all types of graphical documents, but to go back to CAD from that, even eDrawings I wouldn't do it. How about using the free Composer Player instead of eDrawings?
Doug, you can export 3DVia composer files to 3DXml-which will open and display in eDrawings.