Meep--
I've seen one or two discussioons here regarding trying to finesse these issues. The sense I get is that it's a moving target. My own limited experience confirms this.
A couple of impressions from what you reported. On the issue of sample rate, if CD is your original source, then your sound waves are described at 44.1 khz and doubling the samples isn't going to round off any square waves. Note that in college I was a literature major and Proust, Chaucer, etc are all silent on the topic of sample rate, so I'm just winging it here.
If you're going to manipulate the signal (DSP), there might be a benefit, but Matt (jriver) didn't seem to enthusiastic on the idea, from what I read. I would add that converting on the fly to 96 khz adds a whopping CPU load to your playback process, something that is NOT handled by the sound card and which may be to blame for your blips. Watch task manager as you play back. If you're determined to go 96 khz, you might use dbpoweramp to convert your files ahead of time.
You didn't mention bitdepth, and Matt recommended bumping up the bitdepth ahead of any DSP or EQ changes. I won't pretend to understand the concept, but I would note that it's a very light CPU load, so why not.
As you mix and match your output settings, try Direct Sound, and increase the buffer size. These are not MC issues, IMO, as I've had to tweak each card / software / driver config I've ever used.
I'd be interested in your ongoing struggle with ASIO. I'm still using windows drivers, because I got them to work and I'm not going to rock the boat. I run Win2k, but from what I've heard, XP has special issues, both with rumored resampling of OS audio, and with blips in ASIO, FWIW.