Uwe,
Thank you so much for the reply. I found the culprit for the feed dog play - it was a new bolt that came with a binding attachment system. It was not large enough to fit into the hole that moves the feed dogs (See pic). I swapped it for the old screw and the longitudinal feed dog play has reduced from 0.5mm to around 0.1 or 0.2, barely noticeable and a huge improvement.
Regarding the lever bouncing - I'm still at a loss. Your thoughts make a lot of sense - something is rubbing up on something else and the lever's play is the weakest link that allows for a mechanical compensation. The machine stitches very well now, and the bouncing happens the most at the longest stitch lengths. There is an audible click coming from the rear right of the machine on every stitch however, and it coincides with a little jump of the lever. It seems to happen near the middle-end of each stroke cycle, before the needle leaves the material.
Do you have a technical manual for this thing? The service manual just doesn't go into this at all, but I have found some older, far more technical manuals for this machine, they are just hiding behind paywalls to shady websites it seems.