Chosen Solution
When I moved, I somehow managed to get dust inside the headset and onto the display panels. I know it’s not on the lens, because moving the IPD shifts the lenses but not the dust specs. Would replacing two (left and right) eye tube assemblies fix this issue?
Your problem may not be dust, but my in fact be dead pixels. Regardless, both of these are common problems on the Valve Index Dust is much less likely being that the eye’s are sealed with adhesive, but it is still a possibility. Dead pixels are significantly more common on the index due to their choice in components.
To answer your question: Yes replacing both the left and the right eye tube will fix this issue.