Since creating this mod, I have managed to get the cape working after a fashion. Due to the jury-rigged nature of the setup I used, there are now 4 versions of the mod. Two of them are the old versions, the base outfit previously released and a combination of the base outfit with the hair mod for Eresh I've also made. The two new ones are basically these but with the cape added on. All versions that have something besides the base outfit are detailed in the file names.
Note on MoreClothing Compatability: If seeking to import the outfit with cape into MoreClothing, I advise importing the version without the hair. In short, making the cape work as I wanted it to required loading it as a "Static Hair" component (thus rebinding it to another slot works best when rebinding it doesn't drag the actual hairstyle along for the ride). See the MoreClothing notes at the bottom of the resource post for further details, as well as a suggestion on how to input the outfit into MoreClothing.