There is another solution... A bit radical, though. Measure the inside of the hole, or better yet, the size of the tremolo arm. I think it is M 6 or something like that. Then you take, uh what do you guys call it? The tool that you put inside the drill machine to drill holes? But not just drill it, but at the same time carve in, uhm, what the heck is that called then? I am lacking technical terms... You know, a hole with spiral thin inside so you can get a screw in?
Well, drill a hole that is a bit bigger than this one you have. And make a new tremolo arm. If done properly, when screwing it all the way in, it should stop moving easily. Just a thought.