Would it work to remove the last 4-6" of the gray plastic and mount the valve there and upright? You said that it is wider than the plastic, but might it work there with the QDs pointing backward?
You could have the QDs for valves 1 and 3 pointing straight out and have 2 and 4 angled (with 22.5 degree elbows?) up and down enough to clear the QDs next to them.

