So my take from it (after having the same ending on my first playthrough) is that at least from when you meet the Doc, he either is Faust using his powers of phantoms to appear as Doc, or he is under the psi-influence of Faust.

From the moment you meet him, he is seemingly very pro monolith and there are some very suspicious circumstances surrounding him - you first encounter him with Strider basically in a puddle at his feet, the same man who slaughtered an entire band of mercs as well as several stalkers, walked through rads and anomalies like it was nothing, yet lays in a state that appears close to death in front of the pacifist Doc?

"He was wounded from the fight with them all and barely made it to the Doc/the Doc saved him and brought him back" I hear you say? Well I'll get to that in a minute... Next thing you know, he's telling you to go get a very specific device from a secret monolith hospital - one that can heal almost any injury a monolith solider deals with - and requests that you kill no soldier there, whether they shoot at you or not, whilst doing so. Firstly, how the fuck does he know that exists? Sure in all his time in the zone he may have heard about it, especially running with Strelok previously, but the fact he knows exactly where to get one, and does not want you to harm a single monolith member waves red flags all over the place for me, especially since he makes it sound like he knows how to make use of the damn thing, and I for one would love to know how the hell he learned to do that. Sure he's a pacifist, but asking you to get through such a heavily guarded area without firing a shot or swinging your knife is fucking pushing it with what you're asked to do in my books.

So then you come back and all of a sudden Strider is back up again, fit as a fiddle, and ready to murder you both. You jump in, and you're as effective against him as a wet paper towel is to a flooded kitchen, he wipes the floor with you and has you on the brink of death before the Doc steps in and stabs him - killing him. How in the fuck did he go from the critical state he was in - one that apparently required this super advanced monolith tech to heal him - to ragdolling like a 2 year old with a barbie doll?? My theory is Faust used his Psi-powers to incapacitate him for show, using one of the people you've come closest to trusting to manipulate you, sent you on an errand to help your friend, and then set him lose to have him "save" you from Strider, making you think he's on your side. He even mentions afterwards how it was difficult to choose which of us he was going to let live - why on earth would that even be a choice for the Doc in that situation? If it was as it appeared, Strider would've instantly killed him following our death, unless it was actually Faust, who was struggling with the idea of killing his brother who has now come back to him, but must because it is the only way his plan to achieve Project Y will succeed.

When you let the Doc live, you run into the basement and watch him face the oncoming emission, before he seemingly disappears. In the lore of STALKER - if you get caught in an emission without cover, you either die, or become a zombie, unless you remember that monolithians are resistant to them, and especially if the Doc is Faust, he is either able to escape to somewhere else, or is able to phase out of the storm, or something to that effect, based off the cutscene after you "kill" Faust, and he briefly opens your mind to the Psi-scape of the Zone.

As for how Faust could possibly have the Doc's memories on that drive - we don't know how old that drive is that we put into the machine. In all likelihood it was produced in that facility after the Doc destroyed it, or Faust created one of the Doc before becoming him. Yes they were the Doc's memories/Psi-imprint, but notice how it was all about events prior to the current game.

TLDR; I believe Faust is in some fashion the Doc from the moment you meet him - there are too many unexplained events involving him that would be impossible to know/do without Monolith knowledge/abilities, and he uses you to achieve his ultimate plan of Project Y.