Is everyone assuming the shape of the rotary valve is a constant symmetrical shape?
What if it wasn't symmetrical? I.E. the valve would have a tear drop shaped opening (like a camshaft lobe) vs a square shaped opening.
Instead of the camshaft supplying the non linear opening and closing of the valve, the valve itself could supply the non linear opening and closing.
I'm no engineer, but the idea just popped into my head.