Cut path help needed for newbie

I am trying to cut all of the perimeter lines and also the line that runs in the middle of these two parts…I have highlighted the line in parenthesis and with the arrow. I am able to cut just that middle line itself or either all of the perimeter lines…but when designing a cut path and selecting all of the lines to include the middle line as well, the simulator does not show it cutting out the middle line. What are some ideas on how to cut the entire perimeter and also the middle line. Basically with this design, I have one chunk of material and I am wanting to make two pieces, hence the reason I am wanting to cut down the middle after cutting the perimeter. Thank you!

I am attaching the Fusion360 file as well.
cut path help needed fusion360 file.f3d (126.0 KB)

My preferred method, and commonly done in this shop, would be to cut that as two separate parts spaced maybe 1/8" apart instead of the centerline, as surely you’re apt to get a pierce point on one end of that centerline marring the two joining parts. That said, you could probably setup the centerline like this instead, and renumber the start points accordingly?

Ah so extend that middle line in the sketch view and the line being cut that far out is just to prevent pierce point in actual part…very clever! So would I then be able to do all of that in the same cut path ? Or would it be two separate programs that I would be running ?

…all in the same cut path I would think. (BTW my little brain is working in AutoCad 2007 and SheetCam)

I guess I may have to separate the two pieces…even extending the line as shown below, and being able to select the middle line for a cut path, the simulation is indicating that the middle will not get cut. My issue with separating it into two parts is I would be unsure of how to make the two pieces equal in width (after the cut) since I am not cutting neither outside edges but yet the material would be burning off on one part of the other on the inside…if that makes sense.

Hmmm, not sure. I’m, lost when it comes to conFusion360.
I can do it just fine with Autocad and Sheetcam
Maybe someone else with experience can chime in?