I've been thinking for a few weeks now of developing a similar device but purely mechanical.
It'll be two alternately sized gears ganged together on a single shaft to accomodate conflicting focus throws and an offset gearbox to reach the taking lens. Most likely rod mounted. Alternate sized gears for taking lenses would have to be available obviously but 3d printing could facilitate that.
see attached where green represents anamorphic, blue represents taking and purple represents ganged gears to match throws. yellow 1 is idler and 2 is inversion. they would be on an articulating lockable swing away arm.