This solution only was possible because I accidentally placed register A one column further to the right than the diagram indicated. This allowed me to place a ramp that bypassed the 2 bit when the 1 bit was switched from on to off. From there I just traced the paths of which bits would need to be flipped to get to the next multiple of three. I probably should have counted it as 27 parts and put an interceptor at the bottom of register A so that an overflow would be caught.
