The issue turned out to be the IPC fuse (#43 under the hood in my 2010 Silverado).
The fuse was the first thing I checked, but I had only visually inspected it and it appeared intact, so I had moved on to the cluster, ignition switch, etc. After those failed to fix the problem, I tested the fuse and sure enough it failed. Swapped in another fuse, and the whole cluster came back to life.
Feeling silly for losing so much time to an easy fix, but looking forward to how much time this lesson will save me next time I have electrical issues.