It was amazing. Except one thing.
Why did Ulysses think I'm NCR? Is it decided on the reputation with the faction? Why couldn't I tell him I was with House? I wanted a RobCo Courier Duster

The faction Rep is how the game identifies you for a few things, so it would stand to reason that it's where Ulysses would get his impression. It is harder to get the better Strip rep rather than the other factions as there is no real clear quest path for the strip, just a bunch of unrelated misc quests that you have to find.

The thing is, I was both idolized by the Strip and the NCR. Are you telling me there's a Strip route? [censored] hell.
Edit: Checked on the wiki, I only get an Old World Duster with Mr. House, so whatever. I'm still pissed I had to pick "I believe in the NCR derp". This is Fallout 3 level [censored]. I don't believe in the NCR. I'm not saying it's that far from my character, but I'm still pissed as [censored]. Goddammit.

Did you kill Rawr?

NCR rep is prioritized over strip or legion rep.

Some how, I always end up a "Dark Hero" to NCR