Neither swapping the modules nor installing that patch fixed the crashes.

What fixed them was altering a setting in the system BIOS, in the section that handles all of the DRAM timings. Buried in all of the options, just under the CAS latency, was a cryptic option called "performance acceleration mode". The help on the item simply said it would reduce latency between the CPU and memory. It had two options: [Enabled] and [Auto]. I'd always been able to set it to [Enabled] before, but now it's got to be set to [Auto] for the system to work crashfree.

Since the help text is unclear as to what it's accelerating, I'm not sure what performance levels I'm losing by changing it. So I'm not sure if this is a "fix" per se. For all I know, this could be what controls the ability of the memory to work in paired slots, and by setting it to Auto, I'm now losing the performance gain I originally had by using a matched memory pair.

*sigh*.