You should have a look at this - http://www.youtube.com/watch?v=ffK7L0Qj13Q
It shows how thermal paste spreads. Then you can make an informed choice of how to apply it.
And don't be scared to clean off all the thermal paste around the chip. It's best if it's all cleaned from the block and the chip, before reapplying. I'll probably get slated for this, but I tend to use kitchen roll to clean the old stuff off, and a quick spray of isopropyl and clean off to finish. Any fluffy bits left by the kitchen roll is taken care of with an anti-static brush, but a one inch paint brush does just the same. Just make sure you keep yourself grounded, and have no static buildup while cleaning it. I usually earth myself against a pc case thats plugged in, but off, And more recently, I got an anti-static strap. They're cheap to pick up, and worth the peace of mind in my opinion.
Anyway, good luck with the remount, I hope it fixes it. Just make sure there's no other components preventing the block from sitting snugly on the GPU.