Intel's hsf mechanism is one of many reasons why I would never build an intel system. In fact, I should say I could never build an intel system b/c the push-pins are PITA and it's an even bigger pita to correctly install a large cooler, from the way it sounds. I could never do it. So technically, I can only build AMD systems.
Anyway, speaking of thermal grease, remember that AC MX2 is superior to AS5, contrary to pop belief. It's proven to run up to a few degrees cooler, doesn't have any metal particles in it and doesn't have to take time to cure.
Anyway, more OnT, i had bought a ~$5500 system from biohazard that lasted like 4 months, of very light use, and it had a core 2 duo E6300 like the OP has. They intalled a zalman cooler [not sure if they did it correctly; they may, or may not have] and the idle temp started out [with all other variables constant, including same components, nothing altered, nor oc'd and in same room temp] like 19-22C then it would never again go any lower than 28 C idle. Not ever sure what caused it to do that. I just guess it was b/c it's difficult for anyone to install a larger 775 cooler.
Of course, if it didn't die of multi-system failure (medical term; the pc term would be "mutil-component" failure," I guess,) I would've probably lowered the vcore setting since i didn't want to oc.
Needless to say, that's the last time I buy a system that I didn't build myself.