Do you have any cats or dogs? I know I've caught mine eating fish when they jumped, and a few times I've had fish seemingly disappear and I think that's maybe what happened to them.
But as far as the killi being faster, it doesn't really matter. I just put my marble cat in my 220g and there's 3 large tinfoils and there WERE four small tinfoils (I wasn't worried about him eating the smaller ones). Well now there's only two of the small tinfoils left, even though they're much faster than him. I think at night when the tinfoils go to sleep, or are moving slower and can't see well, he catches them, since he's generally awake at night.
If you want a killifish, look into top minnows. They're usually prevalent in most states, and you can net them directly off the top of the water (assuming your state laws allow keeping native wildcaughts). They don't need a big or complicated tank setup and they'll eat stuff like small floating pellets.