I'm sure that putting Shinji in the mental meat-grinder was part of Gendo's plan, too many things in his schemes only worked thanks to Shinji's mental state of the moment(him awakening EVA-01 to retrieve Rei, pulling out the spears from desperation even though Kaworu begged him to stop...)
And I think that it started as early as soon after Yui's contact experiment. Remember that Fuyutsuki told to Shinji that he was there too, but that his memories from the event were erased. Why would someone erase that?
It's possible that Gendo though that Shinji remembering what happened to Yui would threaten his willingness to pilot EVA-01, after all it would be hard to convince him to pilot a giant robot when last time he saw it he "devoured" his mother!
And even if he was only three years old, seeing his mother being absorbed by some sort of giant bio-mechanical monstrosity cut open in the torso area is
not something you forget easily!
Assuming that a retrieval operation was tried like in NGE and that Rei I was born from it, it's possible that Gendo devised a plan by using Shinji and Rei to awake EVA-01 and use it for HIP, but needed that Shinji loses every memory of Yui so that he won't make a too strong connection between Rei and his mother(like "WTF?! Why is she like mom but with blue hair?!"), but still make one on a unconscious level to strengthen their bond(for example when he was meditating just before the run to catch Sahaquiel began, he compared the scent inside of his EVA to Yui's, and then Rei's). That's why he destroyed every photo and belongings of Yui, erased Shinji's memories and abandoned him to his teacher.
You could also push the wickedly even further and think that Gendo also raised Rei on an ostracized environment to make her socially inept, so that when Shinji will arrive, his natural kindness coupled with the subconscious connection with his mother would make him get curious about Rei and try to reach her, while for Rei, Shinji trying to get close to her and being nice(showing genuine concern over her, saving her after Ramiel was defeated, the Miso soup during the aquarium tour, the Bento box he made for her because she never ate during lunch...) would make her latch on him as the one people with Gendo who showed genuine concern over her, culminating in the end of 2.0 when she kamikazed herself just so Shinji won't have to pilot ever again(instead of for the completion of the mission or under Gendo's order), and when Shinji had gone all super Sayian to save her from Zeruel, his will to sacrifice everything, his own life included, triggering EVA-01's awakening.
Just as planned.
Remember that 1.0 showed us that Gendo and even Fuyutsuki didn't had any qualms in using brainwashing on Shinji(Fuyu is even the one who brought the topic!), so using it on a 3-4 years old Shinji to further their plans(while maybe saying to themselves that it's better for Shinji to forget these traumatic events to ease their conscience) don't seems that far fetched to me.
And keeping Rei as "hostage" for the case something in his plan goes wrong and he ends up faced against a vengeful Shinji would also be something I can see Gendo doing...
And if something like that happens, I'm sure that it will be what leads him to his demise : he probably think that Shinji has been broken and abandoned by everyone, and that he don't give a shit about the world or everyone anymore, and will propose to him to join him in launching Instrumentality so he could be reunited with Rei and Yui, the two last persons on Earth that cares for him.
But what he didn't planned is that Shinji managed to find hope and begin to crawl back from his pit of despair in his "destination" that the preview talked about, and learned to actually try to understand the other and care for them, not only because of how he could affect him, but because he learned to genuinely want what's best for them, even if it's not what's best for him. And that other people still cares for him(Asuka, Misato, Sakura, Kaji if he's still alive...) and that he's not going to put his own wishes above everything and everyone else, that even if he want with all his heart to see Yui and Rei again, he won't sacrifice the rest of the world for it and become like Gendo, in an awesome scene that will be the biggest "Fuck you Dad" in anime history, on par with Rei III's "I'm not your doll!" from EoE!
Or... he could make the same thing as in EoE, accept, and once in the giant mental clusterfuck of Instrumentality realize that it's not the right path to follow and abort everything, but that would be a re-hash of EoE and that would be lame, Anno didn't made all these changes just to give us "One more Final bis".