You know, this thread is a POC about something called SOTA+ method, not 3-kang. Usually in literature this is actually a Gaudry-Schost variant, because there cannot be a Kangaroo algorithm that actually goes side-ways, since cycles cannot be part of a Kangaroo algorithm, by definition.

You can read up on the actual 3 and 4 kangaroo algorithm in the original paper from 2012 by Pollard et. co, it's called "Computing discrete logarithms in an interval", maybe you will then notice some of your statements or questions don't make much sense. Also don't forget that 3-kang works on any generic group, and has a lower complexity for groups with fast inversion, like secp256k1. I'm not aware of any papers that take this into account. The rabbit hole is deep.