Don't be offended when people say your workflow is wrong. Your current results are flawed, and that can be partially caused by the workflow. Others share their workflow and you learn by taking the most logical and easy parts and combining them into your own. Just your logics in how you set up a workflow are not enough, with the opinions of a thousand people your workflow can be so much better because they all stack up good arguments you can't just come up with all by yourself. This is the way pipelines develop, through the ages by the speculation of people that talk about their difficulties and methodologies together. SO no need to take offense, we're all here to help
ndchristie is however correct in the fact that it's best to work out key poses entirely, and creating inbetweens and blending frames after, rather than animating a limb entirely and then animating the next limb to match it. Posing starts with placing the hips and then the rest of the torso in a balanced way, then adding feet positions and natural legs from that in a stable non gravity defying position, and the arms are the final detail, creating the actual expression. Then you of course need to tweak and improve, but after that, you've got a single keypose done. Then you go on to the next one, and can start thinking about the inbetween motion and blending of animation.
If you just start animating the legs you won't know how the torso will fit on in a balanced way, if you then animate the arms before you do the torso it'll mismatch even worse. And I think that's what you've been doing, forgetting about the torso, while it is the conjunction of all the limbs, the most important subject to work out properly. Of course any process can be justified and workable, and it's good to be skeptic about things people suggest you, but you should try them before you can say they don't work. I may be completely wrong about your workflow however, so that's for you to work out for yourself
Now on the professor, he just lacks a natural feel and weight. His legs raise and lower at the same speed, but lowering is due to gravity, and lifting due to muscles. Now gravity is much stronger than a muscle, so convey that difference in speed and weight. The current animation is too linear at the arms and legs, and too stiff in the overall. Why don't you rotate his shoulders while moving, and make that coat move alot more due to the body movement underneath?