Use a wide angle when moving, and telephotos when on a stable non-moving base. Telephotos magnify movement, wide angles mask it.
Shoulder rigs still show shake, but help you minimalize it. I just sold mine last night, along with my video tripod.
Think im actually gonna try some DIY stabilizers and sliders. Should be good to go then. Thanks for the tip on the lens. I really didnt even think of that. I was using my 24-70 Sigma f2.8.