I had a similar experience recently and ended up going back to - in my case Illustrator - and remove all the lines I did not need and create a outer line only file. Save it with a name that has ‘cutout’ in the file name so it is easy to find.
Import that onto a what I call a Master slide at the bottom add both files on top of each other to make sure they are perfectly aligned then duplicate the Master slide twice and rename them as detail and cutout and remove what is not needed and then create the cutting path.
Works great for me, I had a project that I ended up with 4 different slides and cnc paths and 3 bit changes on my machine. result was great.
Hope you end up with a perfect project and enjoy making more ones.