So, I cleaned everything out, especially the contacts on the board, and then it sprung to life:
Audio only comes out of one line and the cable has to be wiggled until a sweet spot is reached, but for all intents and purposes this fug-ugly system now works.
I'd like to personally thank Xian Xi, NGT, Lachlan, BWI and everyone else who replied to this thread, as I have got this up and running in a surprisingly fast amount of time thanks to your advice and commentary.
I can now keep running my AES downstairs and this new MVS upstairs, ensuring multiple floors of Neo-Geo goodness.
Thanks again guys!