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Thank you Greg, your suggestion did lead me to victory.
By it self the suggestion was not enough to get a single line. But when breaking up the model in smaller segments and removing a face from an adjacent segment it does lead to a single line being sliced.
When putting back the surface mode to normal then the internal lines dissapear again.
All is well when it ends well.
thanks everyone!
I've updated the thread title to reflect that the problem has been solved.