Can we make an entirely new game mode?
Something like osu! touch, with a separate leaderboard from everyone else. You can probably include phone and tablet players of osu! lazer on here, too, maybe?This is still kind of dipping into the "huge infrastructure change" option, I think.
osu! touch could be catered specifically towards touchscreen players, with allowing multiple inputs at once, kind of like the Love Live mobile game. Except, instead of all the circles sitting around and you waiting for the notes to approach, it plays like osu! standard. Except, it has up to 10 things to press at once. You could even have different types of notes (flick notes, hold notes, etc) to make it more interesting.
The only way for this to work, though, is to make osu! touch feel much more rewarding to play for touchscreen players than osu! standard. If no one cares about it and no one thinks it's worth playing, then this option just becomes a waste of time. But that's the only way I can really think of dealing with this issue (right now, anyways), by making a game mode that people want to play that has an inherently different input setup so that no one can complain about touchscreens having an advantage.