Making an overlapping cut

 From:  Markog (MRAKGR)
10695.1 
I want to do a diff using this curve. I can get it to work if I scale it by 1.001, but that would give me trouble if I ever wanted to fillet in the future since it would create non overlapping edges directly on top of each other. Is it possible to get this to work without having to resort to scaling by a small number?