How about replacing your oval gears with a Double Lamina Compliant Joint? In principle, a DLCJ should be able to replace any gear pair as long as you limit the rotation. That is not a problem with this design. This will get rid of all your backlash without a spring.
BTW, I hate you a little bit now. I am just about to drive myself crazy. It is all I can do not to design a DLCJ that has the properties of an Annirak Drive.
BTW, I hate you a little bit now. I am just about to drive myself crazy. It is all I can do not to design a DLCJ that has the properties of an Annirak Drive.