I have been studying the puzzles for a year now. I was able to comunicate with professor Teske and professor Galbraith, they both worked with professor Pollard, and pointed me in the right direction. I have some questions and some original ideas about the pollard methods.
I understand that you use a base magnitude for the jumps and add a random portion to make the jumps, in a different way for each of the 3 heards, I will study this in detail.
It seems you don't know how it works even after a year. The jump table is the same for all herds, otherwise it won't work.
I'm not able to find an implementation for batch inversion on your code, do you use batch inversion to speed up the computation of the inverses? I understand that in the Classic Pollard method, you can use this approach, computing the next point for a group kangaroo paths. This will make the cost for one inversion only 3 - 4 multiplications? Is that correct?
For CPU code I don't use batch inversion because I tried to make the code as simple as possible. That code demonstrates various methods for ECDLP and loop handling, not optimizations.
For RCKangaroo I use batch inversion, check its CUDA sources.