I recently traced play to the actual shock, (old Manitou Swinger), the actual shock appears to have about 2mm play, worse when air pressure is lower.
When everything is tight there is a slight clunk when I lift the saddle, having spent ages pulling this and that (and getting independent help) I can ‘feel’ (vibration etc) in the shock when I hold the shock and lift the bike – it’s like 2mm of travel is ‘free’ and it just clunks hwne the slack is taken up.
Maybe try pumping it up to a lot and seeing if there is a difference.
Can you mount the shock at one end and try for play.