I liked the idea of hiding the underextrusion by adding another layer, making the side walls 0.8 mm thick. So I printed at 90mm/s and 230C, re-checked the combing enable option.
The result was that the added material amplified the warping problem so much that the print crashed. It was not that the plastic lifted from the tape, it was that the tape lifted from the plexi-glass print bed. I used a brim and when that was printed I added tape on top of the brim that I then folded around the edges of the print bed to hold it in place. No luck, it lifted the whole thing and tore the tape...
My conclusions from all this is:
1. Cura needs to both reduce the number of, often unnecssary, long travels and to add retraction in order to not loose pressure that leads to underextrusion. Or compensate in some other way.
2. Printing a box this large is not possible without a heated bed. Maybe if the temperature is set lower and print speed slower, but then it would take more than 30 hours to print it, in my case.
Luckily I have some of the parts needed to build a heated bed lying around so I might give this print another try some time.
Thanks for all the help, I have learned a lot about printing!