By rearranging the starting setup, I was able reduce the number of parts to 29:
This works the same as the book solution, so pull the red lever to start:
…Look, I just like diagonal counters, okay? 
3 Likes
I like your varitation of the puzzle 42 very much. In case anyone is interested in reducing the number of parts in @RingTheBell’s variation to 28 parts, please see below minor modification:
https://lodev.org/jstumble/?board=rre0e0e0l0le0l0le0l0lerrlleerxlfirfeerfeelee1_16_16
Pull red lever.
2 Likes
This can be reduced to 26 parts - if bending the left register is acceptable 
https://lodev.org/jstumble/?board=000l0l0l0lerr0lee0xleerxlfirfeerfeerfeelee1_16_16
2 Likes
Why stop there? Why not bend it all the way around? 
https://lodev.org/jstumble/?board=lrleer1f0r1ee0lr1e0ler10leerilfrlfexfelrf_16_16
2 Likes