Hi Alan
I had a similar problem with my Burns trem. My solution was to fit a slightly longer cap head screw, a half nut to lock this to the collar on the trem plate and 2 half nuts to lock the arm to the screw. There is still a little bit of wobble but hardly anything and I could probably improve on this by replacing the fibre washers with nylon or maybe thin metal ones. The arm ends a up around 2mm (the thickness of a half nut) higher than originally.
I have a few spare screws and nuts so if anyone needs to try this send me a PM and a set is yours for the cost of postage.
Roger