I think it's a great question. (and, I'm behind on my TIME reading too).
Here's my initial response, especially because these ideas about reducing the experience of "self" or "perception of self" to neurons made me think about the experiments of French Impressionist artists during the late 19th century. (seems like a stretch as first, but just follow me for a second...)
Painters like Monet and Renior were trying to capture light in their canvases; they painted very quickly with dabs of color and fast brushstrokes to capture a moment in time, the "impression" of light on a landscape as seen by the human eye. They wanted to bypass the subjectivity of the artist (their personal interpretation of "tree") and capture the scientific effect of light on the actual tree (light "impressed" on the eye's retina).
So, one day Monet and Renoir go to the same frog pond, set up their easels, and paint the same "impression" of the landscape from the exact same angle. Same stimuli, same neurons firing.
But, when you look at thier canvases, they're quite different. Some individual subjectivity found its way into each painting. They were more than what their eye could record.
We are more than our biological existence. And if I ever doubt that, there are many museums full of art that give me evidence of a world beyond mere scientific fact.
(I hope these links turn into images.)
Monet's
La Grenouillere
Renoir's
La Grenouillere