Those 'coincidences' are foreseen matters in the dead sea scrolls. Did you forget SEELE has knowledge of the arrival of angels?
The Dead Sea Scrolls have always struck me as being more of a guide than a set of precise predictions. All Seele knew was that the Angels would be coming, and the various ways to initiate an impact. They didn't have specifics about the Angels, or the exact dates of their arrivals. If they did, why would they let Gendo, the man they employ to head the fight against the Angels, go to the moon when an Angel's arrival was imminent? Why let 03 be infected?
[quote[I don't know what she did to it, or anything about its nature. It is clearly more than an audio playback device. That's the whole reason Mari targeted it in the first place.[/quote]
We've never seen the SDAT do anything but
play music. The only reasons it's important to the plot are that Shinji uses it to distract himself from reality, and he attaches sentiment to it.
She didn't just randomly parachute onto Shinji. Mari is a spy character, sabotaging things is in her nature.
It's possible that she placed a listening device on it, but I don't see how that breaks any time loops.
But hey, maybe I'm biased... I get that you want NGE to connect to RoE, but personally, I prefer the idea of it being a completely different retelling. No time loops or anything.