I finally figured out what the Media Monkey add-on is doing that MusicBee is not (currently). It just has a command that loops a parameter over all the selected tracks.
In that script, %O is the full file path of the selected track, which I believe is equivalent to <URL> in MusicBee. So you can either run the application once for each track with parameter %O in the command line or you can run the application ONLY once and loop the parameter as many times as there are tracks, with a specified separator. They way they represent it is <%O: >, where <> tells it to loop the parameter and whatever's on the other side of : is the separator (in this case just a space).
I looked pretty closely at the current MusicBee functions and don't see a way to achieve this. I'm hoping it would be fairly easy to set up... *fingers crossed*