That's puzzling. I guess now I'm nervous because I'm starting on rebuilding my 1990 KitchenAid now that the new tub support came in, and I went ahead and ordered a new set of upper and lower snubber pads. Maybe I should keep the old ones if they're in okay shape, which they seem to be from the initial test runs before doing any disassembly.
Could you try cleaning all your pads and the contact areas that they rub against with a strong alcohol, as well as the brake bell under the tub support? It seems like the brake is also slipping if it's letting the basket move slightly, and maybe there's just enough slickness somewhere to allow more movement than designed. That's the only thing I can think of from what I see in your videos. It's understandable to be worried about it doing that though, because over time it could stress the cable connections or yank your water level tube out and end up leaking out all over the place.