This is interesting---things seem to have gotten much, much better after I went from the 64-bit version of MPC-HT to the 32-bit version. Apparently, the drivers are more stable in that edition.
I (finally) also figured out how to bitstream to my receiver, and that seems to have stopped the clicks and pops, but now I notice weird, subtle stutters in the audio stream.
By far the worst problem is how the card seems to be picking up some kind of interference from the PC in the rear channels in games. Depending on the game, I will get buzzing, pops, or a very annoying whine from my rear speakers. I'm pretty sure it has something to do with the fact that my rears are powered by an external amp running a very high gain (ground loop issue, probably), but it's weird because the noise will go away completely if I do certain things, like pause the game or bring up a menu. The HDMI audio stream isn't interrupted when I do such things, but the interference oddly goes away.