PROGRESS REPORT
I unplugged everything I could from the back of the PC, and that bought me 40% more free processor. I also downloaded the RATTV3 tool, but for some reason on my machine it's not giving me a driver-by-driver breakdown. There's a good description of both DPCLatencyChecker and RATTV3 here.
The best tool I've found so far is LatencyMon, which basically does everything that the preceding two tools do, without making you think. The download page asks you to register via email - but nothing happened for me when I did that - but you can scroll to the bottom of the page to download anyway.