After installing my new Ultima 90 heatsink (check this thread), I found out from a member of the forum who had run tests that re-orienting it might yield better temps - so I did it:
Here's what the paste looked like after removing the heatsink:
So I decided to draw a slightly larger line of paste this time:
I also asked if there were any pins behind the LGA 775 socket and here's a photo if anyone else wants to know (there are none that could be crushed):
Everything installed back into the case:
Temps are indeed lower. Even when running FurMark and OCCT together, the CPU temp doesn't raise above the minimum detectable temp (it did before).