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Re. Handwarmers: Wouldn't that be illegal? As you could theoretically hide some illegal substance in there to doctor the ball? Like when a pitcher has a stain on his hands and people go crazy.
The statistical tool that you were looking for in your discussion of aces is basically an independent samples t-test. You are saying that you know the mean (each pitcher's ERA) and imposing some sort of distribution and then drawing randomly from those distributions. Basically the question that you are asking is that if Verlander is really better than... me, how often would we be able to detect that in a small sampling frame (1 game). That's a question of statistical power. (For the initiated, in a t-test, it's 1-beta.)
I think the worst case in shuffling your rotation regularly is that you would end up getting less than 34 starts out of your ace over the course of the season. Would the small increased likelihood of winning that one game defray the cost of not pitching your ace the most times during the season, or screwing with his rest days?