They shipped the little washers in the box, with the recommendation to use them when connecting 2 gear bits, but leave them off when connecting 3 gear bits.
My impression is that the main design flaw with Turing Tumble is the steep board angle, and it would have worked a bit better if designed for a 45° (or something) board. That and using heavier rotating parts with a bit higher moment of inertia. But I think it’s still great despite the occasional malfunctioning part.
As for frustrated kids: I think interaction with an adult who could notice parts sometimes malfunctioning (and correct them on the spot) would probably help forestall some frustration. But my kid is only 4.5 so we have to do the puzzles together.
While my memory is fuzzy, it was indeed crossovers which caused majority of undeterminism, at least in the set I had. There are some alternative 3d-printable implementations if you walk by the links there. I didn't try.
Hopefully, Spintronics would be more reliable, given that the author is well aware of the unreliability issue with Turing Tumble.