I found some new ways to break the game.
You can gain a lot of speed by pressing the left arrow in the frame between stages. The most consistent way to get the timing right is to stop at the end of the level, turn around, then press forward, and as you pass though to the next stage, press the back arrow. And if you hold both arrow keys you can maintain the speed. It allowed me to skip some areas where you normally have to stop and wait.
I also found you can get extra height from the springs if you hold down arrow as you run over them. I use this on the level with the upper deck guarded by spikes.
Thanks to Laxxius for finding the skip in the starting room. Saves about 1.5 seconds.
I had one run that was faster (2m 35s) but wasn't recording. I believe it's possible to go sub 2:30 with these strats.
mod note: retimed with framecount and IGT