OK, you've lost me. Maybe a line diagrem would help. To me, a quad breaker means 4 20A breakers. Do I understand correctly that you have 2 regular 20A 120V circuits, and then a 240V circuit which you split at the receptable end? Are you sure you have 240V across the 2 center breakers?
I'm positive, but here's a couple more pictures. I double checked before I finalized the big plan over on the DIY forum, then went to Home Depot and narrowed down the plan with what was available to best suit my box/space requirements.
I appreciate you double checking though. Things like this can be a real hazard if not done correctly!