Another point against mentioning Vader at the beginning is that there’s no reason to believe Rey would know of his immaculate conception, so it feels more like Kylo is talking to the audience rather than Rey, since he’s basically using Vader to explain the concept. On the hangar scene it feels more like he’s revealing to Rey that his grandfather had the same origin as her, explaining their connection.

Despite what I said earlier about Kylo having visions of Rey, I like the way you worded it, since it sounds more like a recent vision similar to how Rey saw Kylo in the forest when she touched the saber. Maybe it could be something like: “Before we met, I had a vision of a girl. It was you, in the forest. When we fought, the power inside of you awoke. You revealed yourself not only to me, but to Palpatine… just as he’d intended”. Still not sold on the idea, but it’s better.