I think there is a suggestion for you.
To quote where you wrote,
"there's a thin layer of thermal paste on the GPU",
you will need to apply more.
The gap between the GPU core and the heatsink is far too wide for just a thin coat of thermal paste.
You will need to purchase a copper shim, or plate to fit in between. You will need a plate about 0.6-0.7mm thick. 0.7 is readily available on ebay. Apply the thin coat of thermal paste to each side of the copper plate and seat it between the GPU core and the heatsink. It will work perfectly.