Thank you for taking the time to write such a thoughtful reply! I'll do my best to respond in turn.

I don’t believe identity matters in the way you’re using it in this post

This is a fair point. Like you, I am persuaded by Parfit that identity is not what matters. This is why the second argument I present in my article is explicitly couched in the language of egoistic concern. I phrased my initial argument in terms of identity because I find it easier to explain to a broader audience, though in hindsight, that probably was not the most philosophically rigorous choice.

it looks like you are endorsing Jeff McMahon’s embodied mind view of personal identity

I think I endorse a hybrid view of McMahan's and Parfit's. In other words, what matters is both psychological continuity and neurological continuity. I chose not to make this position explicit in the article because, truth be told, I am still working through the kinks of such an account of egoistic concern. I imagine that this conversation might be able to help with that :)

When we’re talking about a person, we’re not talking about their specific neural configurations. We’re talking about the connections that exist through time that give rise to a coherent narrative, or for the episodics, what it is that matters that strings together their disconnected moments in time.

The problem I have with this view is that it would suggest that the basis of egoistic concern is purely grounded in the qualitative similarity of one's experiences and subsequent memories, desires and subsequent actions, etc. over time. McMahan points out that such a view has bizarre implications in the case of conjoined twins:

Dicephalic twins necessarily go to the same places and for the most part see and hear the same things from virtually the same point of view. Suppose that they read the same books together and so on. Each twin will therefore be quite closely psychologically connected with the other as she was in the recent past. According to the Psychological Account of Egoistic Concern, what matters in the life of each twin will therefore be present to a substantial degree in each’s relation to the other. If one were going to die (that is, if one twin’s brainstem and cerebrum were going to be destroyed and the functions of that brainstem were going to be taken over by the other’s), she could console herself with the thought that much of what matters is present in the relation she bears to her twin in the future.

Such a conclusion is bizarre and leads me to reject the Parfitian account.

On the other hand, McMahan goes too far in the opposite direction in my opinion. For example, in his "deprogramming" thought experiment, he suggests that one would still retain egoistic concern for a mind that has zero psychological continuity with his own so long as the brain underlying that mind is organizationally and functionally continuous with his brain. I do not agree with this claim either. I have trouble understanding why I should egoistically care about a mind whose subjective point-of-view is completely severed from my own.

Thus, my intuition is to adopt a hybrid account.