Hi Eldar, I like it, simple, in expensive.
There are a few products out there such as the Fly Cam, Steady Cam etc, mostly made for Video use, but also mostly entailing a hinge vest and arm arrangement.
As you mentioned, the 200-400f/4 brings a few small issues to the Party now, when hand holding it's a bit of a task operating the Zoom and Converter as well as the Camera, maybe we are looking at it from the wrong perspective.
Perhaps we should be looking at stabilising the Subject ??