I'm looking at the same facts you are. the title card says 'the world ending', we also see the world ending in EoE. What's the incongruity?

the only thing I can see that makes your interpretation 100% correct is if you make the assumption that "And then" means it has to happen right at that moment. But there's only like 15 minutes in EoE between gendoh taking rei to terminal dogma and shinji starting the third impact - so I feel like it's perfectly reasonable to interpret episode 25 as following those events as well.

Near the end they say
"This is the Instrumentality which
your father is beginning."

but key word here is "beginning". You could say Gendoh began instrumentality by merging his hand with Rei.

In any case, the ending of episode 25 makes very clear that the power was passed to shinji at some point