"Mahogany and some Hard Maple and probably a piece of rosewood..."

My choice would be the maple or mahogany -- whichever one is closest to the size you need, or you can even go by the grain direction (lengthwise is much better than crossways, and get as close to quarter-sawn as you can get).

I would avoid the rosewood, simply because it's harder to glue well, due to the oils in the wood. I know modern glues can do it, but why add a complication?

Bob