This is a really interesting concept, well done!
After playing it a couple of times, it does seem to settle quickly into a single strategy - keep the two lanes pointing straight up at all times. Thinking through some possible solutions:
1) Offset the input and output lanes so it's not just a straight line.
2) Add some blocked spaces into the grid of belts so there are obstacles that need to be navigated around.
3) Freeze the belts for a couple of seconds after changing them so that the player has to react to the change
4) Enable more input lanes as the game goes on, ramping up the difficulty.
Really minor, but having the randomization aspect always move a UP to a LEFT means that I can consistently triple click to fix it to UP. Randomizing how rotated a belt gets would force more thinking.
I'd love to see how this turns out with a little more time :)