Yeah, that’s pretty much what I’m thinking.
I personally don’t see any reason for how my actions (or, possibly, lack of actions) should be justifiable or not justifiable on the basis of “moral intuitions” and “not moral intuitions.” (The whole idea of EA is motivated by having certain intuitions, which are not wrong, just unlike most of my actual opinions, which are wrong.)
The most useful way I can describe my views is “accept the premise that it is better to be a good person than a bad one, and work on a subset of problems that are not connected to this premise.” There’s no “moral intuitions” problem, there’s no “moral intuitions” problem, there’s no problem with selfishly pursuing your own goals, etc.
I think that's a fair summary of the way I look at it. The actual way I look at it is less "which problems are not connected to this premise" and more "which problems are connected to this premise, and which problems don't have this premise as part of their underlying concept."
Let me try to say this in different words, perhaps more helpful to others than to me:
I don't see the "moral intuitions" problem as big a deal. I see it as the exception that proves the rule. People have always acted morally, usually without even realizing that. We simply need to learn how to use a formal moral system, as they do, to get a better handle on the world. The notion that our intuitions might not be right is simply one more challenge for us to overcome, not the rule.
For example, suppose I think that there is a lot of suffering in the world, and I want to do something about it. If I just use my own moral intuitions as a guide, I am likely to come up with reasons why my efforts to help the world would cause it to get worse, and this would be an instance of the "moral intuitions" problem. If I want to do the most good with the information I have, I need to learn about the world and about human behavior.
A lot of people (myself included) like to tell stories about how they "found God/the light of reason" in the form of a book, or in reading certain authors, and then they were like "aha, I'm not an atheist any more" and that was that. Actually, I think that "finding God/the light of reason" can be a more gradual process than that, and it's important to recognize that even when you're doing the best you can.
So I guess what I'm saying is that for a lot of people, the idea of being an atheist is the norm rather than the exception, so it can be easier to get your head around the idea of being a moral non-realist than it is to get your head around the idea of not taking moral realism as the norm rather than the exception.