I'd take it a step further and and go with a slot. Closer to the structure of the 2 circles with the ease of a slit. I am surprised the operator/programmer of the machine didn't suggest something like your idea or mine, since it is common practice for them to make engineering designs more manufacture-able/structurally sound. (Source: I used to program water jets and was constantly re-designing parts sent by engineers/designers.)

Also, I would definitely move towards die-cutting once he settled on a final design, but with his sense of tinkering, I doubt he'll ever have a 'final' design.