Sounds good. I like to play games that confuse my brain.
There could be 4 input modes to this mod, and Osu! could randomly switch between them every 10-30 seconds during a game, when there is a one second pause or higher on a beatmap. There could be an image that pops up on the screen telling us what input method the mod has switched to.
The four input methods would be.
1) X = Normal, Y = Normal
2) X = Normal, Y = Reversed
3) X = Reversed, Y = Normal
4) X = Reversed, Y = Reversed
In addition to the four input methods I've mentioned above, the game screen could randomly rotate and zoom in and out, at different directions and speeds, in time to the music. With all of these features on one mod, I guarantee this would be the most difficult mod to master, and it would make the flashlight mod feel very easy in comparison.
As for the issue of having random games each time we play on a beatmap, since this would cause problems when using the mod for ranking purposes. A set of text files could be stored on the Osu server, one text file for each beatmap. Then when a person plays a beatmap online with the mod enabled, the person would download the text file off the Osu! server. And if the person hasn't got the text file and they are playing the beatmap offline, Osu! would just generate a random game for practicing on, with no multiplier score added.