An option for the conversion utility that removes the original files and replaces them with the converted files.
It could be a simple checkbox added next to "output to folder": "same as the original file". An additional checkbox could let you delete the original file.
If you replace the files, MusicBee could make sure that all the tags are copied to the converted files (maybe as a post-conversion step), add the new files to the music library, skip the inbox and update the location for all the playlists that included the original files.