The only tunnel (581 meters) between Cologne and Copenhagen is at Lengerich (52.189722, 7.8525). There are some between Liege and Dueren. Speed behind Muenster and Dortmund (via Hannover) to Hamburg Harburg is often 125 miles an hour. The route via Hannover is nice of that you travel through a "mountain" range where the river Weser has made a path at Porta Westfalica (52.216667, 8.933333).
The solution should be easy; do the return not on the route you went in the other direction. The route with 2 faces is Muenster to Osnabrueck. First 125 miles till Lengerich and than come the curves till Osnabrueck, when speed is greatly reduced with 2 90 degrees curves to the left and shortly later to the right in Lengerich.
We're not returning! To give a little context, I'm on holiday with my dad and brother (who is rather interested in history), touring a part of Europe in a week — this has become a sort of tradition, since we did one last year and the year before.
This year we flew to Copenhagen (which is where I was born — my parents were living in Denmark for a few years for work-related reasons) and we're making our way to Lille to catch the Eurostar (which is something I requested since I haven't done Eurostar before as far as I remember). My brother is interested in history so we'll be spending a day exploring the site of the Battle of the Bulge. The rest of the time we've been spending doing various things around the cities involved. Obviously I have to balance my rail enthusiast needs with my family's!
I did, however, thoroughly enjoy the train ferry. I'd recommend that, though perhaps go in the off season when it won't be as busy as it was today...
Thanks very much for all the help you've provided; I forgot to mention that before. It's been very useful for determining what we can and can't do with our ticket! We'll probably spend Wednesday making our way south, stopping for a couple of hours at a couple of the bigger/more historically interesting cities, I expect. After we get to Cologne I suspect we'll try to make our way to Libramont where there are buses to Bastogne which is the bit my brother is interested in. Then we'll be heading to Ypres on the final day, before making our way to Lille.