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I'm not sure/can't remember if they can spawn in maps with very low bonus prizes or through other methods, but even if it's possible, your best bet is still every X0 floor in the item world for its consistency.
Also, you should probably ask in the steam discussion/board, not just because you have the PC version, but I think it's more active there?
To my knowledge, there isn't a way to get Mr. Gency Exits other than completing a floor in the item world that's a multiple of ten. If you need Mr. Gency Exits, I suggest you try to go into the item world with items that have the Manager, Armsmaster, Mentor, or Broker specialists, and subdue them. You'll want them later if you plan on playing past the main story. You can then exit by defeating all enemies in floor 10, 20, or 30, then going to Innocent Town and talking to the ghost to escape, or selecting the escape option if you're not warped to Innocent Town.