Ah I see now, I was thinking the parts to the Rhs 'flipped' vertically not horizontally. Ok two things. Do not mix heat sink compound and flexible heat sink interfaces (the grey pad). Use one or the other not both.
As you know you need an absolute flat face to face 'surface to heatsink' interface. I can see the idea of putting a coin between the top of the chip and the lower surface of the grey pad, but, from what you have said I think a piece of flat metal would be better so the suggestion of a flat piece of metal foil would seem a good one. Good luck.
Ps. I can't see what the graphics chip is but it looks as though it has soldered edge contacts around all four sides. If you can get a powerful magnifying glass carefully look at the soldered edge connections. In the past I have found chips that had been unsoldered or 'dry jointed' connections and if you see one, and have a suitable soldering iron, you can usually touch them up even though they are very small.