I think the legs rhythm-off moving in the double bounce is because of my silly experiment: I try to change the key poses (contact, squash, pass, overshoot and contact again) for the standart walkcycle, making overshoot pose as a second low in the walkcycle, so there is appear of two lows (squash and overshoot) and two highs (contact and pass), but for legs is too much messy, and I think that better to learn the specific double bounce key poses. Silly me!
I understand your advices about tired walk and I will try to make it more up and down with falling down at each step. I try to avoid back and forth movements because I have no experience and for now back/forth seems like a pigeon walk

Only in the sneak walk I can make this trick.
And yes I'll keep it up because it's not so hard (one or half hour for each cycle). The really hard thing is to notice the issues. So thank you, Mathias for advices.