I found the cause of the issue. It was not Explorers of Fortune after all. It was the single Action Replay code that I use, which allows guaranteed recruitment.
Even though the code only activates after a button combination and can be turned off with another, simply having it enabled in the emulator was enough to interfere with ALL dungeon restrictions (recruitment, EXP, and Level 1 behavior), most likely because it just hooks into the code of the game. I can't believe it didn't occur to me, especially when I was recruiting Pokémon in Temporal Tower (even though it was "off"). Disabling the cheat completely restored the intended behavior.
I'm sincerely sorry for the confusion in those last two pages, given this was the ridiculous reason of my issues with the hack. And thank you and other people who might have been testing as well. The somewhat good news I suppose is that if someone happens to use the same code someday and runs into the same issues, they might run into my messages and get it resolved.