I like to keep my heavy limb woods pretty thin, and let the majority of my limb stack be bamboo or maple. If your outer lams are fairly thin, you can use pretty much whatever you want. There are a lot of really fine custom bowyers using osage, cocobolo, and bocote in their outer lams. They work just fine.
I recommend you find some maple, elm, or walnut for your core lams Dick. They are readily available and make really fine core woods.