Agree 100% with you here on the damping of the outstretched arm.
If you would make your body rigid and long from toe to fingertip with an outstretched arm like a long plank,than that shape will damped the temporary disturbances of the pull and the recovering weight more.
I find that the pull is mostly responsible for the bobbing, depending how hard you pull offcourse.
You really have to shape and accelerate your pull in a certain way to move forward in a more or less straight line with minimal bobbing.
It tells you often that your normal stroke has quite some sideways or up and down force components.
I have no footage of myself executing it properly. Still cant do it 100% properly also.
Sometimes its nearly there and feels wonderfull and smooth. Its getting better and better though. Feels more and more like normal swimming, but just with one arm less.
I like to do the easier version that is swimming 75% with one side and let the other side go along for the ride, help do the other 25 %
Than you still are close to normal swimming, with the recovering weight keeping you in the same rhythm, but only using the weight of the arm on the non working side in the recovery, also hardly any pulling on the non working side.
Its a bit like loping then, big pull and hip action on one side, limp fillup action at the other side.
Gives most of the benefits, buts easier to stay aligned and keep the rhythm going.
If you then try to go from 75 % one side to 90 % one side for instance, you can feel where it starts to break down and work on that part.
she also has a great one arm freestyle.(and normal)