Hickory can handle some runout, obviously less is more in this case. How about a pic of the wood?
Fujimo had a great idea about sawing up the wood to reduce grain runout.
For the core, any maple, or elm, or oak, or walnut, or probably any other hardwood is fine. Pick something that looks nice and isn't too heavy. I've used hickory, doesn't seem to slow things down appreciably.
For the belly, personally I like to use stuff that is fairly dense andprimarily use ipe. Also have used jatoba with good success, shedua with success on a lighter bow, and wenge as well. Obviously just like any other wood bow, the lighter the belly wood is, the wider it needs to be.
If you can get ahold of hickory, you could make the thing out of three lams of hickory. That will defiantly work, just should be made a bit wider than an Osage or ipe bow.