"push that 125 closer to its limits before upgrading"
LOL
I know a few riders that can outride people with 600s using 250s and 125s. While this isn't completely true, but if a 125 or 250 still has massive chicken strips...you know they're doing it wrong and not ready to upgrade unless all they give two ***** about is straight line acceleration.
OP: I would STRONGLY suggest that you take an honest look at your tires and see how much of the sides you haven't used. SS bikes amplify your mistakes, sometimes in very unforgiving ways. Upgrading to a 250, 500, or 650 would be a great idea but I would recommend you stay away from an SS. But again, if all you care about is being able to go really quick in a straight line...then go get a 1000 lol