If you don't want to hear me waffle on just skip to the question at the end.

Okay so I'm finally going to make a character I mentioned here a while ago that uses energy weapons and maximises action points (and by that, I mean achieves the actual maximum allowable by the game short of General Oliver's Uniform). For this I need the Fighting Chance duster, however I want to in the end side with the NCR (they'll wear the duster to humiliate the Legion more with their defection and betrayal). I've only done two favourable things for the NCR so far (fixing the generator and Snuffles' foot in Sloan) but I'm approaching the Boulder City Showdown which I want to do as it's logical to attempt it when it first crops up in the story as opposed to leaving it after Lonesome Road - and I want to do it diplomatically. I have a suspicion this will earn me the Accepted rep, so...

Will I get the Fighting Chance Courier Duster at the end of Lonesome Road if I'm Accepted by the NCR but Liked by the Legion?

From what I know, it goes by your highest reputation, so unless you are idolized by the Strip, you may likely get the fighting chance duster.

That's what I've read too and thanks for the incredibly speedy reply, but I wanted to double check as it is incredibly irritating to attempt to optimise a build only to find it un-optimisable because you didn't prepare fully. I'll assume everything's okay, but maybe keep a save before Boulder City just in case (still, the back-tracking if it's not okay and having to redo the entirety of Lonesome Road would probably kill off my enthusiasm).

Just get the NCR rep up, and after meeting House but before going into LR, do I fought the law and defend the gangers from the NCR, that should drop your rep to wild child.

Yeah you will get the NCR duster with that Rep. Even if you have more rep on the strip, you'll still get the NCR duster (you only get the yes man duster if you neutral or less rep with NCR and Legion and Strip).

But yeah, you get whichever is higher rep, in one playthrough I was accepted by the Legion and Idolized by the NCR and Strip and I got NCR duster.

No because I do want to stomp on the Powder Gangers too. The ending I'm shooting for is the alliance of the NCR with the Brotherhood, being Idolized by both (hence choosing the ending in Lonesome Road where I stop the nukes entirely - which I don't think I've ever done beyond one character where I tested all the endings to see the slides).

If both Legion and strip were idolized, but NCR is wild child, which one do you get? Not that I care, the duster effects are not that great in the end.

You'll get the legion duster that way. If the factions are tied for top rep, you get the duster in order of "NCR, Legion, Strip". So you'll only get the strip one if it's higher rep then both NCR and Legion, if it's tied with either of them then you dont get it.

Note that you can somewhat cheat the system. If you wear a faction armour your rep with that faction is set to neutral while it's equipped. So if you were idolized by legion and strip but wild child with NCR, if you wore a Legion disguise before getting the duster, you will get the House Duster.