Great info, thank you.
Let's start with the platform in the first image...
If you've tried adding some kind of absorption under the tripod and also tried adding weight and you're still getting vibrations/shaking, then it sounds like the platform may be where it's happening. You may want to try reinforcing the platform by adding mass to it. A cheap test is to just add a bunch of heavy stuff to the top of the platform (without overloading it or making it dangerous, obviously) and see if that has any affect. If so, then you know you need to beef up the platform.
Another option is to find a way to mount the tripod or camera stand directly to the concrete floor, but this would require purchasing a new tripod/stand that can reach much higher than what you have now.
So I would start with the platforms and see what you can do there first.