Sorry to doublepost, but yes. You can only do the quest once-per find. You can find it on any difficulty though and play it on a different difficulty, so if your really wanting it, just speed run normal Gurhacia or Ozette.
Your looking at a 2% chance of it popping up in a dead end. On average you'll see about 2-3 dead ends per floor, so 4-6 per run of an entire area. Its still random, but expect to do at least 30 or so runs before you find it again.
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