For now, here are the steps to use Edge output in Muse.
Put all output files generated from Edge in the same folder that you want to export Muse output files. (keep all the subfolder structure e.g. edge_includes
In Muse, use Object->Insert HTML... menu to insert the following code:
"Project-Header-r1v1.html" is a HTML file name that part of your Edge output.
Do not copy and paste the content in "Project-Header-r1v1.html" file directly since this refers to different jQuery file and it will also cause a duplicate Javascript include which break the output.