haven't got much time right now, so just a short text
after reading your text, i'm not exactly sure if you'd rather create your walk ani as a straight profile or slightly towards the viewer, as in your idle stance.
however it may be, i'd suggest you try not to create each limb's animation separately, but as a whole. looking only at a moving leg, it's hard to tell if it's gonna work out good or not.
i would try to go from animating a rough version of the full body, to refining the details after that. one way to do it (that's how i do it sometimes) is (if you have layers in your software), you create a separate layer for let's say, the head, the torso, one for each hand, one for each foot (not connected to the body with limbs yet). for a starting position of these body elements you can put your idle stance as a ref underneath. then you do a frame by frame ani of the unconnected elements (which would result in something looking like Rayman). once you're happy with how this animation looks, you try and add the limbs and neck etc. in between for each frame.
but of course, that's just one possibility.