I know this sounds delusional but Donald Knuth is giving a lecture at Stanford (where I live btw) in 3 weeks and I believe that if he knew about my research, he'd likely bring it up. It'd be the biggest honor of my life if he did.

His lecture is called "Adventures with Knight's Tours", and the -very brief- abstract specifically mentions minimizing the number of oblique-angle moves.

My research is about minimizing non-straight-angle moves; it couldn't be a better fit.

But, apparently, there's no way to contact Knuth. Sad.