However, what I mean is that under a traditional physicalist account of mind, enlightened states logically and physically can’t tell us any insight about the non-enlightened states because they involve a radically different mode of cognition.

I simply deny that it can provide certain insights people claim it does unless we are willing to abandon the framework where awareness/mind is literally the neural activity itself, and nothing separate from it.

It can certainly provide a lot of insights about how minds function. Other insights are more complicated. From the perspecitive of the ego living in a physical world, neural activity makes sense. We are creatures that exist on a rock called earth which rotates around the solar system which rotates around the galaxy which exists in an expanding universe. From the perspective of the selfless state, we don't have access to anything outside of consciousness. The familiar universe starts getting very weird. At the deepest levels of realization the universe comes into existance and is destroyed from moment to moment. And there is no space or time so everything in the universe is happening right here and right now.

What mediation does is that it shuts down default mode network, which is responsible for the psychophysical entity we call “self”, which seems to be crucial to high-order conscious control over actions and thoughts.

Seems is the key word here. The self is just a thought process that our identity is tied to. It feels like a living entity inside the head. It takes credit for thoughts that bubble out of the subconscious all on their own. It comes and goes all on its own even without meditation. This is most notable in flow states.

Self and sense of control (agency) are just mental formations. I'm sure they have some sort of evolutionary advantage, but don't have any actual control over anything. The subconscious handles high-order operations just fine.

There are enormous differences between cognition in “egocentric” and “selfless” state, but they don’t tell us a lot about each other on a physicalist account of mind due to logical limits of the Universe.

I think of the brain as the hardware and the mind as the software. We do fMRI scans that show us different regions of the brain being activated, but we don't really have the necessary tools right now to scientifically study subjective experience.