So, Ulysess' dialogue, how does it work with reputations?
Which one is prioritized? The one with the highest reputation?
If I have high NCR and I want Vegas dialogue should I kill an NCR soldier or two to get it down to mixed?
Does Vegas dialogue include Freeside or is it just The Strip?

Simply, how does this dialogue work`?
I've only done LSR once with my Legion companion.
So with my independence Courier I want Vegas dialogue.

if you want indy you'll have to have low with the strip, ncr, and legion. If you have the strip high he says your with house, if you have ncr high he says your with ncr, and if legion is high he says your with legion, but if all of them are low (around wild child) he say your indy.

NCR= NCR rep is highest
Indy= Negative Strip Rep
Legion= Legion rep is highest
House= Strip is highest

As a side note for when/if you ever do a House playthrough, it's best to intentionally keep your NCR rep at accepted until after you do LR in House's footsteps. The reason is that though all titles have the same levels of Rep, Numerically, NCR can go higher than Strip rep, so if you're idolised by House AND NCR, you'd get NCR dialogue.

The indy dialogue is elusive. I found from personal experience that having equal, negative reputation with the Legion, Strip, and NCR along with House being dead will grant you the indy dialogue.

I had a reputation of soft-hearted devil with the three big factions when I finally got the Independent dialogue, so try to do that if possible.

Well, I tried killing members of Strip, Legion and NCR, got to the lowest mixed reputation I could, but when I talked to Ulysses, I got no [Independent] dialogue, he said I walked without a flag though, but I got no dialogue options for it.

I'm not positive but maybe you need to up your reputation with some of the Indie factions (like the Great Khans, BoS, etc.) or that's how it's supposed to be.

If you go the Indy route, you don't get any rep based dialog with him until the very end.

That is the Indy dialogue. To clarify, Indy dialogue comes from neutral to bad reputation with Strip, NCR and Legion.

Well its very complicated. Why should a guy that wants to make Vegas Independent want to have a low rep with the Strip? Stupid.

He doesn't care about making the Mojave independent, all he cares about is that it doesn't fall into the hands of the NCR, Legion or House. It also makes sense that a low Strip reputation is needed for Independent dialogue since the Strip contains the three families who are all loyal to House.

But they are his pawns.
House is also fully aware of Benny's plot.
He knows the Omertas are planning something but doesn't know what (why he sends you).
The WGS was a last minute decision brought on by you, so it's not like he would have predicted that.

Yeah, I was idolized by the Strip and liked by NCR, and it was fine until the final battle where my only options at the end were the option that resulted in me fighting Ulysses, and an NCR dialogue option. It would be nice if they would just give you the option to pick your side at the beginning of LR and skip the confusing reputation crap.

He makes comments on having no flag, so actually you have just about the same amount of dialogue as the other three.