If I had recognized the encoding as Base-64, I would have investigated it as such. As it stands, I had no idea what the encoding was (I thought it was some UTF-specific shenanigans).
had mentioned on #perl that any MIME reader should be able to grok it, but I have no experience with the MIME::* modules. It wasn't until I looked at MIME::Parser that I followed the trail that led me to my goal.