I also think it's possible the neons died, and then the bettas and other fish ate them, but it is interesting that after you removed the sorority girl who was getting picked on, the neons went missing. Of course that could be a complete coincidence, and maybe something non betta related happened to those three. While you might never know for sure what happened, the only ways I can think of to try to find out would be to A) Set up a video camera (a camera that takes pictures at regular intervals should work too) next to the tank and check the footage to see if anything happens or B) Remove all the bettas, and if more fish disappear after removing the bettas, you will know for sure it was not the bettas. Of course, if you remove the bettas and nothing happens, that doesn't mean it was definately the bettas, it could just mean something happened to those three, and the other fish ate them. You'll have to play fishy detective and try to unravel the mystery of the vanishing fish! ;)
Is it possible they maybe got sucked into the filter, stuck in some crevice somewhere in the tank, or escaped out of some tiny space? If a fish or two ... or three escaped (which sounds improbable to me but I guess it could happen) I wouldn't put it past a hungry pet if you have any, like cat, dog, ferret, etc. to eat a fish that lept from the tank, which might explain how fish could just disappear.