So I'm going to focus on this part, since the rest of it is a lot of details and discussion on ideas that are probably best discussed a little further down the line.
The intention with this is that Doof is, put simply, doing a doublethink. Doof is mentally compartmentalizing the stuff he's doing in DEI as separate from the Doofania thing. One is his company, and the other is the rulership of the Tri-State-Area. And you may say that doesn't realy make sense...and you'd be right. He isn't really thinking clearly or rational about the latter thing, because as mentioned, it comes from a sort of a load bearing trauma, a blind spot. The thing that makes Doofania as a concept hard for Doof to approach is that it comes from a deeply unhealthy part of his worldview.
The chain of logic goes something along the lines of:
People don't hate me -> People hating me is a natural state of affairs -> If this is the case, there must be something unnatural that is causing people to like me -> Success and power is admirable -> I am successful and powerful -> This success and power must translate into me having forced people to like me at some point -> I did say I took over the Tri-State-Area -> I own the Tri-State-Area, and because of that people in there like me because they have to.
It's emotional reasoning worming its way into his logical reasoning and twisting the result he comes to. This is what we, as the QMs, mean when we talk about Doofania in the confines of the story. It's also why the Council doesn't ping, because Doof considers them close to him (not friends, who would be friends with Heinz Doofenshmirtz?) and values their opinions. And they care about what the public think, and you know what, Doof isn't quite sure as to what mysterious whims the Public judges him by, but not being hated is nice, you know? And of course, most of this is unconscious anyways, so that's another layer to it.
So that's how Doof thinks about it, really. He doesn't. It's a kind of dissonance that is unpleasant, so he avoids it. He's been getting better about that, but as it turns out, the man who avoided thinking about a robot that was his son for years on end may be a bit slow to process and confront his own feelings.
I hope this explanation helps.