I thought it would be something like this.
Most people don't take the time to understand his argument.
On your first thing: He big idea isn't that social institutions are not reified, mind-independent things, his point is that these idea can manifest themselves in the real world by hijacking someone's mind.
An example is if someone is raised with the idea that they have to dress a very specific way because of God. While there is a parent to enforce this it's not a spook, but when this person becomes independent they continue to dress this way.
The physical enforcer (the parent) is removed you can see that there is still something forcing this person to dress this way. If the person decides to not dress this way they might feel bad or upset because they disobeyed God and their parents. That's the spook enforcing its law.
If the person said "I'm not going to dress like that, it's just stupid" then they have cast off the spook. They realize there is no real reason to follow it. The thing that caused real things to happen had no real power.
Stirner is trying to get people to free their minds from these. His thing is that people should do what they want to do. If the same guy from before wants to wear the clothes because he likes them, then it's not a spook; it's a choice and there is a real reason for it.
You say his self-interest isn't reducible to non-spooky statements, but this is a complete misunderstanding of his claim. Nietzche's self-interest is a spook because people who buy into it feel that this is want they "should do" and there are things they "have to" do if they want to be an ubermensch.
Stirner's self-interest is the absence of spooks. If you want to be nice and donate money or whatever, then you can do that so long as you do it because you want to and not because you feel like you should or because it "the right thing" to do.
His thing is about being free in the mind and doing things you really want. Thinking that you must make the most money or that you can't be empathetic are spook and not what Stirner is advocating.
If you think that people are inherently evil and cruel, then you might think Stirner is arguing for those things. I don't think people are inherently evil. Stirner would have just thought of "evil" as another spook because trying to avoid or trying to become evil is a thought that will change the way you act and take away your freedom.