I wanted the gears to shift properly (90° with no flipping back a bit) but I wanted a solution I could apply without taking the model apart.
I have a ton of axle 2 notched so I put one in each red thing:
This works perfectly and can be applied without too much trouble. The inner one is a little harder to insert but it's doable with a creative use of another long axle and an axle connector.
Continuing to build to verify it will work with the body added.