"Adequate levels of weirdness" is a metric I'm always shooting for, but didn't have a name for. Thanks!
I wasn't sure if having an in-game cursor would be necessary, but it sounds like it would.
It should be at least 3 times taller than the default Windows mouse cursor, and should have a contrast layer, so that it will be clearly visible, regardless of what colors are behind it.
So, iow, if you make it a black cursor, it should be surrounded by a white layer. If you make it sky blue, put a dark color around it instead.