If you used a fuel with a higher specific gravity, won't that just make it run richer? Then you'll have to lean out the mixture a bit.
I wouldn't think it would give you more power as long as the injectors were still capable of injecting a greater amount of lower density fuel. I'd imagine we're limited mostly by the amount of air we can get into the engine, and the higher octane of race fuel is the main advantage. Does that sound about right to you?