MCEBuddy may be possible but will require extensive customization from your side, use the AllowH264CopyRemuxing and then creating a custom profile using Handbrake or FFMPEG using the copy codec - feel free to play with it. Keep the EDL file allong
with the original file and MCEBuddy will use it which will save you time, so essentially it should be pretty quick with the right config - but no guarantee it'll work, never tried it.
the other way would be to use MP4Box to add the EDL file as a chapter to the file manually (you'll need to convert the EDL file to Chapter files first).