Ok - I've tried this fix today using Anadin tablet packaging.
Instead of slotting the shim into the slot as per the OP, which I found impossible to do, I put them under the screw head. My rise was pretty much in the centre of the left side, so I only used two shims under the middle two screws.
I made the shims as 2 small squares, with the hole in the centre. I then pushed/ wedged the removed screws into the holes and trimmed off all corners to leave a circle of the shim material just larger than the screw head. I then screwed down the screws to just tight, with no extra force.
I have no bulge on the silver bezel. The back doesn't fit as exactly as it did, but there is only a very slight gap (less than .5mm).
the screen is now solid, no clicks or sounds when pressure is applied, and it is flush with the bezel.
I've streamed some HD TV, played 50 mins of Dead Trigger, 1 hour of Riptide GP, and got the heat up in the unit, and no problems so far. Screen still flush.