First of all, this all reads just fine in terms of understanding; you've got all the facts straight. Yes, time flowed at different speeds between the First and the Source; roughly the Flood of Light was in 3.4-ish. Time presumably wasn't always flowing faster on the First, but it was flowing faster in that period; you won't get much pushback if you said that it was moving slower just before then, for example.

As for how to make the trip, the main struggle is that the 'normal method' doesn't work; the equivalent of voidgates don't really function here. However, there are some options, depending on what exactly feels like it fits for your character. Immediately off the top of my head without checking for further ideas...
  1. There are the, for want of a better term, 'gate mages' from the caster role quests. We don't have much info on them, but that does plausibly mean you can say that one of them took a WILD shot.
  2. Like you said, Fairy Nonsense is always on the table. They weren't at full Il Mheg-level power before the Flood, but according to the Traverse they did exist.
  3. If something deliberate is more your speed, I'd say the most likely culprit is probably Ronka; we can tell they had some pretty serious juice, and thanks to the Great Serpent(s) they're already on sort of a 'suspicion list'.
  4. Judging by the Pilgrim's Traverse and the good old lineup of wacky hunting logs, you could make a plausible case that SOMETHING out there was capable of that.
  5. If all else fails, there is the applicable answer of 'sometimes rifts just happen'. If it's good enough for Clive, Noctis, and even the permanent Omega/Arkveld crossover fights, it's good enough for RP. Hell, it's possibly what happened to cause the Nier raids to happen!