What ddgonzal says is right.It is the ability to raise the compression without detonation that yields the increase in power.

Generally the engine will run cooler which may be a real benefit.

Methanol has an octane rating of about 108 . As for racing fuel that will depend on who supplies it so you need to check the Octane rating with them. You should also realise that LPG has an octane rating of around 112. A purpose built dedicated gas only engine may be worth investigating.