I have not finished mounting mine so I have zero experience with your issue. But I'm watching this with keen interest for rather obvious reasons. Some comments and questions for you to ponder.
I confess that thousandths jitter doesn't surprise me. Hundredths does.
In my ignorance, I would think that machine shake would not matter much if the shake happens on the reader head and scale simultaneously. However, if either one is mounted with some flexibility relative to the other, any movement is gunna show up. So I'd be looking to see which one can move how much.
If you turn off the machine and press on the system components, you might be able to zero in on what is moving where.
Acceleration and force usually bend things WAY more than is obvious. Put a dial indicator almost anyplace on big stuff and watch the needle move as you lean on things. Stress and strain are ALWAYS present no matter how big something is.
There doesn't appear to be any strain relief on your cable. If it is shaking, it will shake the reader head. Try constraining the cable.
Your description of how your system is mounted isn't clear to me nor are the photos. Can you take a few more photos and/or add a drawing?
More specifically, the size and length and resistance to motion and force of the mounting brackets in various axis would be a concern of mine. I see lots of pictures on the web of people mounting things on long thin brackets. Maybe they have to do that, but I'd avoid it if possible.
Other generally speaking things to consider:
Twice the thickness = 1/2 the movement.
1/2 the length = 1/2 the movement
1/2 the suspended mass = 1/2 the movement
When you are talking about steel or aluminium, and mere thousands of an inch, it's hard to visualize movement. Try imagining the components and brackets to be made of rubber and take a critical look at them again.
Also, consider harmonics. What happens when you run the machine at different speeds?
Edit - Apparently aligning the bar code on the scale and the bar code of the reader is also important. If they are not aligned, the last set of digits are more likely to flicker.