Thanks chazers18 and GruensFroeschli for your replies.
I don't see any major differences between your posts and mine. I'm thinking that I might have miss-configured something in the routing or nating on one of the boxes.
As a follow up, RDC also 'kinda works'. I can connect to one machine (of the two that I tried so far). That being said the connection is unusable; it drops in and out, doesn't hardly refresh, and is unresponsive to input.
I am thinking about merging the functionality of the two machines to see if that fixes this. It should simplify things at least…
Oh well, wish me luck.