Been in the deep end quite a few times. I held on during, don't think I ever lost conscious awareness or 'blacked out', or w/e that word exactly means.
I'll give my opinion:
I think 'spending lifetimes' or 'thousands of years' is fanciful speak, a personal play on words, something slabbed onto the enormity - especially the impossibility that the time dilation can reach in terms of it's subjective effect, perceptual and otherwise.
I think in ways it's a gross oversimplification - it's easy to say that sort of statement in terms of description, almost an effortless description in ways.
Though I've said similar in a couple of my reports years back, especially with the strongest experience I'd ever had - wherever I was taken, I was gone gone.., and the lives thing, yeah - I lived ..uhhh ..an endless amount? Thousands? Yeah, probably. It was alot within that given timeframe of the experience. In that experience ..I held on man, for real, it didn't lose me during. I was there for it fully.
They were all split second, it was constant for most of the entire experience, and I wont ever forget it. I still remember it.
They were all woven into the experience and all it's constantly morphing permutations and moments. It was the most powerful experience in my entire life.
What was it? Heck if I know
That experience was sort've akin to taking an elevator:
up ,up , up, out, out, out, forever.
Children, families, beautiful clear scenery of the outdoors, people dying, people being born, groups of people laughing having good times, the rest ..there was so much.. can't speak beyond this really (also wrapped within the essence of hyperspace - the aesthetic of it, of the experience itself).
Felt like the ultimate summercamp