Di-624 is know to cause problem on certain firmware. I suggest you update to latest version, and set the gamer mode option to enabled.
Thanks for the advice. Sadly, I am updated to the latest version I know of (version 2.76, released back in 2006, I guess this is not a supported product any more) and gaming mode is turned on. I tried fiddling with the uPNP setting, as I've heard that causes trouble, but no luck there either.
I discovered some kind of a bug in my router where it would not let me forward a range because it kept telling me a port in the range was already involved in another forwarding rule. That port was nowhere to be found in any range or in any screen anywhere I looked on the router.
Hm, this seems a bit different in that the router is 100% convinced that the port is being forwarded.
So, being a bit more fresh this morning, I had an idea: I deleted the "forward port 6008" rule and created it again. Now the port is open according to the forwarding checker. I even managed to get past the connecting screen and into a Pantheon game for the first time in ages, but "a player has left the game" at the loading screen and the other team was down one person and had an AI, so I dropped to even the teams.