Hope you're just practicing critique and that you're not pissed of, because I take an opposing position, my mentor
I know, that taking Construction from Oracle was, and almost always is a mistake. I know exactly, that I found a reason for it to do so in that round though, may have been that I had to make a blind-pick, or that I just saw Mansa researching it at that turn, and thought "well, I need Elephants anyway on this map, if I want to have a fair chance at conquering it" .
What you must not underestimate, is, that Elephants are way more powerful, and that it was already really hard to conquer the map with them. It might be, that Immortals would have had a chance if used like you said (so for choking) various AIs and not allowing them to get Metals, but I don't think, that there ever was a chance for that, as the war against Lizzy already took everything, Peter had Hills-cities, and you know how fast Deity-AIs tech towards Longbows.
I admit though, that choking aswell as Worker-stealing is a weak spot of my game. It's extremely powerful, and I always try, but often enough, the AI I try at, has Metals hooked before my Warrior even reaches them, or they're creative and their workers don't show up at the outer ring's tiles, or, their land has many Forrests, and I have not only to search their Workers, but to also follow them sometimes, and once they begin chopping, I think twice about it, as AI in war builds up just so many Forces. I know, lure them on the open field, but that doesn't help, if 5 Archers have the order to defend the city, and 5 Archers take a lot of Immortals.
Getting the Shrine with the 1st GP also wasn't planned, but product of GP-Pollution by Oracle. I could decide, to either get the GS in time with CS, or having to wait 12-15 turns, and often enough, I succeed with taking chances.
The point I wanted to make, was, that Incans just have an extreme synergy with the game, and the timeline, resulting in a lot more hammers. These hammers allow for World-Wonders like the one's you built (imo the only really important one's, besides Kremlin later) . Those World-Wonders allow for an Economy, that's beyond what normal empires can do. I just tried to build the GLH with Cathy in a game on epic-speed, it was impossible! I only rexed to 2 cities, researched only BW + Sailing, 2pop-whipped the Lighthouse with max-OF and chain-chopped with 3 Workers afterwards, still I got beaten (1900 BC) . Next game, I tried for Pyramids and / or Oracle, both went 2400 BC (never seen Mids at that time, but De Gaulle builds them really often in my latest games) . I'd maybe have had a chance at both of them, if they would have gone later, but not without crippling my whole expansion.
I'm just playing a game with Catherine again, where there were no chances at stealing Workers, no chances at any Wonder, and even though I divert the grand part of my Ressources to expansion and development, I have 6 cities, while the AI have up to 9. There wouldn't have been even a chance to build either an army, or to have more cities, or even Wonders without sacrificing something really important, and this is just where the Incans are impossible to beat.
They don't build a Worker, they begin with Quechuas -> City grows
Then the Quechuas steal the Workers, the city has already grown -> Instant

+

They then conquer an AIs capital, saving them the need to build a Settler, and getting a really really good location at 3300 BC. A normal Civ takes until 3000 BC 'til they can produce their first Settler, and it'll be in a medicore Location. The new city will also not be size 4 and rock from the start, but be size 1.
Even if one has begun on stealing Workers at that time with the normal Civ, the Incans have simply killed their target already, while it had only 2 Archers / city. The initial Worker costed something, the city is smaller, Immortals are more expensive (this is without rexing to a 2nd city, so Darius, for "totally normal Civs" , it's even worse) , they reach their targets later -> more defending Archers -> less time to produce troops from the conquered city / less troops in general due to higher losses and lower hammer-efficiency.
I hope, I made it clear this time, what I mean. I'm not trying to push this game down, it's absolutely brilliant, but there is no Civ as powerful as Incans on Marathon Settings. Even on the best map and with pristine play, a normal Civ will never be able to make up for the things I mentioned.
If you think different, please either tell, or show, because I know you're the best, but I've become quite good too, and we're either talking of 2 different things, or your using tactics I'm unaware of, and that I need and want to know!
S.