It's really a complex equation of things to come up with "what will fix the problem". It seems that the two things possibly at issue here are the sound card/driver and/or the CPU. USB devices "tend to" use more resources than some other things, so a great driver is really needed, especially if you are doing a lot with a bunch of channels at once, but if you are at the mix part of things and are just using the stereo out of that card, it would seem ok from the data throughput perspective. That doesn't rule it out as the issue, however, especially since you are running a bunch of tracks with a bunch of plugs at 96k. The 96k part CAN be helpful from a low latency achievable point of view, but not necessarily for overall performance at high load. That's a lot of bits/bytes to push around.
The CPU is certainly suspect as well - and you know your options there. Unfortunately, a motherboard/CPU replacement is a non-trivial upgrade. Sure, it's easy enough to snap it all together, but to really do it right, you would have to rebuild the OS/apps/etc since the motherboard has some many functions - busses, cpu, memory, etc. It would probably "work" if you just swapped it out once Windows figured it out, but it would be less than optimal and you may lose whatever gains you were hoping to get in the process. It's better than it used to be under earlier versions of Windows, but I still wouldn't recommend doing it that way.
You said you have had other similar projects work, right? Is it at all possible that there is just something wrong with the project or some plugin that's loading or something? I've had projects that misbehaved with what seemed to be a lower requirement than other tunes that were absolutely more complex from all perspectives and determined that there was just something wrong. It isn't easy to find or really to fix, but in the end, it was the only way I was able to complete the song: export the tracks, bring them into a new project and start adding everything back in one at a time. Is there a "breaking point"? can you "archive" (as in mute/solo/archive) some of the tracks a bit at a time and see if something drastically reduces the issues/cpu usage/whatever?
Hope this helps in some way.