Ok, since the clearing is not that much, I can give you an idea but you'll need to go to a person who has a grinder on him (mechanic, Machine tool chap or a simple fabricator) Take the heat sink you removed from your GPU and just grind about 5mm off the top of the card....(Fins)
Better still if you can, provided that the base of the heat sink is thick, grind off 2 or 3 mm off the base and the remaining off the top.....:)
Of course you''ll need a good machinist for the second option since the base must be pretty smooth.
But in case they have a slightly protruding square at the base of the heatsink to make contact with the Core Chip on the GPU, then I'd advice you to get some thermal tape and use it around the chip so as to avoid the heatsink metal from making contact with any contact(soldered) onto the PCB in turn avoiding a short on the card....
Don't do the second option..... it's a crazy shaped Heatsink
and it'll interfere with some PCB components (Thats why the crazy shape) Best option is either use a grinder to get rid of 5mm from the top of the Heatsink fins, or if you're good with a metallic saw or file, then you can DIY .