Do not bother spreading out the thermal paste. You can end up with air pockets if you thin it out imperfectly. It doesn't take a big air pocket to screw things up. I just put a blob of paste on the center of the core and let the mounting pressure squish out the excess. I've easily had hundreds of CPU and GPU mounts using this process and no problems with ambient and sub-ambient cooling solutions.
I have to agree I swore my the thin and spread method for years but it is very easy to get wrong. I use more than a grain of rice maybe halfway between a grain of rice and a small pea. Put it in the center, attach the backplate FIRST (it holds the heatsink in good contact w/ GPU) and then apply the GPU backspreader. Tighten the screws down in a start pattern halfway then go back and tighten them down all the way once again in star pattern (i.e. upper left, lower right, upper right, lower left)