Maybe it should but I don't think it will.
The problem with the servers all thinking that their public port is 4569 is that then the registration system will advertise them with the wrong port unless other steps are taken to modify the registration info. At least that is what I ran into when I first tried to do it years ago like you suggested. I found the simple fix was to have each server on a different port, same as Andy is saying. Maybe now the registration servers are newer and improved and they pick up NATed ports during registration. I don't know.
I am a dinosaur, I know it. I am CCIE2285 I helped write some of the code that runs in Cisco routers. I greatly improved the IPV4 NAT code in Cisco routers (in the beginning) and really made it work well and scale better. Most of the advanced NAT features that I designed are still in all Cisco routers and L3 switches but are not used because almost no one knows how to configure them. So I have to disagree about NAT being evil. It is wonderful if you know how to configure it.
I watched the video. Sorry, there currently is no IPV6 in the voter board or the RTCM but they are still very useful. Maybe you can write the IPV6 for them.
I am aware of a couple of bugs in the app_rpt.c that were never fixed by Jim despite me identifying them and what was causing them.
Yours could be related and I will look for my notes about what I had found and see if those parts of the code are still the same.
One of the bugs I had tracked down was a bug that under specific situations would send all transmit audio out over the links including local only audio like IDs and tones. Apparently, I was the only one who experienced it even though Jim could reproduce it with my info. As I remember he gave me the "locallist" and "locallinknodes" commands to work around the bug. That was too long ago and I don't still have the configurations that needed that and I don't see any documentation for them so I will have to dig through notes from long ago to re-find that info. As I recall, I think it was a sequence of keydowns back and forth between the linked local nodes aligning with an ID that would induce the strange problems reliably every time. Unlinking the permalinks and re-linking would fix it until the next time. Now I have separate computers for each node so it isn't an issue for me now like it was back then.
While typing this little pieces of memory are coming back to me. Maybe after my regeneration cycle tonight I will remember it all. Maybe I have jogged someone else's memory who can fix this before I can remember it.
Chuck