I made progress. That’s another half Saturday wasted 
Just came home from an ARCing trip outside So the thing is this:
- The IP address and forwarded port works. I can connect with ARC just fine from the wifi in the corner cafe. (So all the info in the ARC tab of the remote, and the telnet test via cable internet, and port scans via websites, etc., did show the correct result - the Core and its internet connection are OK)
- However, no dice over Vodafone Germany’s phone network. Drove the bike a bit to also ensure I am in a different cell tower area. All the same, I can’t reach the core’s external IP from the phone network. (So the telnet test when being tethered to the phone’s internet also showed the correct result - fail). I also tried with a different SIM from a different contract (but also VF) in a different phone, same issue.
Next step: Vodafone technical support. I already talked to them in the morning and was lucky to have a lady who understood what I was talking about. She flipped some switches in the settings for my SIM, but that didn’t help yet, and for this case she gave me a way to contact them back, so I don’t have to tell them the whole story again. And armed with my new results, I think we have zeroed in on where the problem is.