I upgraded to 32 GB of RAM, and no longer have this issue, though I'm still on a 7200 RPM HDD. This supports my theory that it was a paging issue.
I also noticed before the upgrade that my cursor specifically had to be over one of the tasks on the taskbar, for that task to unfreeze. I don't know how to prove this, but my theory is that hovering the mouse over a task initiates a thread to generate a window preview, which in turn places that task at a higher priority slot in the scheduler. Without this scheduler boost, it was stuck in a lower-priority queue due to its having been paged. (Though, I would imagine paging schedulers use some form of MRU prioritization algorithm, so I don't know why the task was deprioritized so much...)