I am pleased to announce that I am typing this on a freshly installed Vista64 installation, on the same exact machine that I had so much trouble with recently!
A genius Tester in Windows contacted me with a theory and a possible work-around, and he was right: something about the AHCI driver is unhappy on my machine, so his suggestion was to go into the BIOS, go to SATA Operation and change it from RAID Automatic/AHCI to Combo mode. I did this, and Vista installed in less than 30 minutes! Fabulous. It was a bit freaky to see the percentage for "Expanding files" change every few seconds, instead of every 15 minutes in all my previous attempts. The downside is that my XP installation that I dual-boot to will blue-screen with the BIOS set this way (for the reasons outlined in an earlier posting), so when I switch OSes I have to also switch SATA modes.
I'd like to link to some Dell documentation on this particular BIOS setting, but I can't find any.
The default install covered all my hardware except audio: I found an XP64 driver and tried installing that, but it complained that I was using the wrong operating system. However after that Windows said "You want me to try that again with some compatibility settings", so I said Yes, and it worked! I have a working audio driver now. My Performance score is 3.4, which isn't great, but will suffice for what I need (and for what I paid for this box).
Next I have to start installing the most commonly used stuff and trying to see what I can and can't do in this brave new Vista world. It would be nice to get XP to boot in Combo mode, and it would also be nice to delete the ten or so dead entries in the Vista boot loader left over from my installation attempts, but that's just gravy.