I'm thinking that, maybe more than damping or other adjustments, you may want to source some sleeves and collars that will replicate what parts #140 and #150 are supposed to do? There should be no play anywhere, yet the shock needs to be able to rotate slightly at its mounting points due to the arc the rear wheel travels in (from a side view) as the suspended wheel moves up and down through the stroke of the suspension... if that makes sense?!
In other words, you don't just want the shock eye clamped tightly from the sides, but free enough that it's able to rotate slightly around the bolt passing through it. So - rotating slightly around the bolt, but with no slop on either side-to-side or up and down movement (or anywhere else).
Hope my 2 cents help!