Re: which cam software can do this?
Try the Trace function in Fusion 360, that's how I would do it. This forces the tool path to do exactly what you want. I use this for odd shapes sometimes if Fusion doesn't do what I want.
I'm also pretty sure some of the other 3D cutting functions will do this also. Fusion requires a little prodding occasionally to produce the desired result.
If you can post the F3D file (most likely will require you to zip it), then I'll be happy to see if I can torture Fusion into cutting this.
Jim Dawson
Sandy, Oregon, USA