Warning, huge dollops of interpretation ahead.
I think part of the thing with Cloud is, he's imitating what he thinks a hero is SUPPOSED to be, not necessarily accurate to how Zack was. IMO he comes off more like Sephiroth than Zack, which to me says a lot about his subconscious--that maybe even though Sephiroth betrayed him he still views Sephiroth as the thing to be emulated, because Sephiroth was strong, because Sephiroth wouldn't have gotten gunned down in the mud. And Sephiroth's much more like Cloud, personality-wise. Easier to be him. The Zack bits are the physical, shallow things, like the style of movement; things he couldn't have picked up from Sephiroth because he just wasn't around him enough.
And yeah, I'm purposely describing this as a somewhat-deliberate process. Yes, I think Cloud's a jillion kinds of messed up at the beginning of the game, but I also think he's receptive to being rebuilt, as it were. He's unhappy with the person that he is. I actually think his conscious participation in the farce is what allows him to hold onto that "real" bit of himself--because he's not entirely being "controlled" or "manipulated," he is controlling and manipulating. On some level he does know what he's doing.
Which is to say, I'm on the side that says separating fake!Cloud from real!Cloud doesn't really make sense. One is a construction of the other (that is later appropriated by Sephiroth for his own ends, but that's even less connected to the LTD than this post and oh my god look at the time).