Yeah, that video is pretty awesome, I fudged my way into a similar solution a few months ago. When he was saying the devil is in the details and that it takes a lot of tuning, that's exactly what he was talking about. It took me a few weeks solid to get a similar game mechanic in Unity to work(was my first time working with physics like that). And I don't think I watched that video first. It can work but you pretty much have to find all of those values for yourself, expose all of them that you can in the editor and just start playing with different values until they start behaving. If it's just wobbling when it's not moving, you could always turn some of the physics forces off when at rest.
Make sure you are applying the correct types of force, i.e. https://docs.unity3d.com/ScriptReference/ForceMode.html They are each very different, and sometimes they operate differently than you might think they will, unless you really have it down. Experiment with them.
I can say that starting small helps, only apply one force at a time(or group of them 4 corners/etc.) and only apply the minimal force you need to achieve the desired effect. Then add another force(or counter force) and tune it, then re-tune the first force because they will probably effect each other. Then when both of those are working perfectly, add another, and tune all 3 to work together.. etc.. etc.. It can be a little tedious. But worth it.
Hope it helps, if you get stuck with some specific code, feel free to post it up. Lots of smart folks around here.
*Damper: The way I think about damper is that you're restricting the speed at which something can move or "bounce".
If you are trying to dampen a force, then you have to apply an opposite force that is a certain amount LESS than the force it is attempting to counter or (dampen).
Oh yeah, you can also create some nice dampening effects by modifying the rigidbody drag values.