The problems being that Unit 01 isn't there, and that it's rather peculiar to have Rei take an active role that doesn't involve her collecting his soul.
Kaworu and Yui can both appear to Gendo. Both Adam and Eva-01 are merged with Lilith at this time, and Lilith exhibits an ability to appear anywhere (despite being physically located in Kanto) -- so we can probably assume that Adam and Eva are taking advantage of the same mechanisms that Lilith is.
We're given a transition with Yui, from pink blouse to purple turtleneck, and the only real purpose of this would be to link her with Eva-01 and let us know that, yes, she's acting as Gendo's spirit guide here. The exact logistics don't matter, because we're dealing with gods and they can do whatever the movie wants them to do.
Rei 3 standing there at the end has her hands posed as if she's holding something, but whatever it is we can't see it. This brings the image of Lilith holding the Black Moon to mind, but I don't think this is pointless miming -- rather, it's a clue. Lilith holds the collected souls of humanity between her palms -- so here, at Gendo's special induction ceremony, what could this manifestation of Rei be holding but Gendo's soul? This may seem paradoxical, if Eva-01 already obtained the soul by eating it, but assuming Yui is only able to manifest on the spot by piggybacking off Lilith's AATF, then everything pans out.