You Cannot Ride This 'Backwards Brains Bicycle'

I remember experiencing the opposite situation, where something I understood and had muscle memory for was mixed up by trying to think about it too hard. For example, when I learned more about the idea behind counter steering on a bicycle, I suddenly had a trouble steering if I thought about it too hard, even though previously I intuitively was already doing it.

Thanks to my multiple-layout typing, I actually know the trick to being able to switch your motor controls back and forth. What you need is strong contextual hints. The fewer visual, tactile, etc., differences, the harder it is for you. If the reverse-steering bike was dramatically different than every normal bike, it would be much easier to switch between them. But since it's practically identical to regular bikes, it's vastly harder for your mind to distinguish when to apply each different motor skill pathway.

I'd try modifying the reverse-geared bike with drop/racing handlebars, painted a unique color, hornless seat, streamers, etc. In fact starting with a recumbent bike would probably work pretty well. Alternatively, you could (probably) manage it by only ever riding your reverse-geared bike on one or two certain road/trail/paths, and NEVER riding a regular bicycle down those same locations. If they are sufficiently obviously different than each other, you won't get confused.

Propeller-driven fighter planes had similar issues. The centrifugal force of the spinning prop and heavy rotary engine meant the controls responded 90 degrees offset. Lots of pilots crashed for no other reason than being unable to re-train their reflexes.