For running, you could try speeding up this animation...
If you're going to rework it, maybe these videos will serve as inspiration:(From 1:23)As I see it, in the first video, it's something like a gallop (the front and rear limbs work alternately, although not entirely symmetrically), and in the second, the gorilla practically switches to running on its hind legs, only occasionally using its front limbs for balance, but not pushing off with them. And it's also punching a pear, which is awesome...