All right, so, I switched to using a Chesnaught since he's not immune to Poison, Paralysis or Sleep, but now I can't check to see whether they have Effect Spore or Regenerator (I was previously using a Carbink with Skill Swap and watching as they hit me with Feint Attack; very tedious, but also accurate since I can guarantee I have Effect Spore). The chances of them having Regenerator, though, are quite low.
So, using Power-Up Punch, Poison Jab, and a few instances of Wood Hammer, I've hit 39 of them, with not a single status condition.
Afterwards, I switched over to my Doublade and hit the last one with False Swipe. After 9 freaking hits, I was finally put to sleep. Switched back to Chesnaught to finish it off with Poison Jab. Still nothing. (I'm holding a Metronome, and I don't have the hidden ability. Doublade's got an Eviolite.)