It seems you are correct. The problem is simple (sort of), but unexpected.
I accidentally discovered I can make the problem appear/disappear by applying pressure to the top of the SRAM. In one case, I managed to crash the machine that way, evident because the "heart-beat" indicator (an LED indirectly driven by the IRQ line) went completely dark—it is normally dim until some IRQ-intensive activity occurs, e.g., serial I/O.
So it would seem I have a mechanical problem, not an electrical or timing issue. With that revelation, I put on the high-powered magnifiers (8X) and carefully examined the SRAM, which is an SOJ32 package. As near as I can tell, all joints look pristine, with the soldering having nice radii where the tucked-under J-leads meet up with the PCB pads.
As the soldering looks to be okay, it could be there is some "debris" under the SRAM that is creating an intermittent short of some kind. I can't see in there, so it's only supposition. The other possibility is the SRAM has an internal data pin connection that is disturbed by pressure on the package.
Either way, it appears replacement of the SRAM will be required to ferret out the problem, a task that I can't carry out.