Considering messing around with building a board bow. From what I've gathered, it seems red oak is most popular, but it requires wide flat limbs. What kinds of wood would allow for narrower, straighter, and deeper core limbs, or can that be had with red oak as well?

I'd be looking for around 70" bow drawing 45 lbs at 29-30 inches.

At 70", you can take red oak down to 1 1/4" in. If you want to go shorter than 70", osage is excellent. You'll have more compression in that design so you need a wood that is strong in compression, dense woods are best. There are lots of woods that will work, red oak is usually used because those of us building board bows are usually better off using inexpensive wood.  

If you do use red oak, try to get a piece with thick late growth rings. The more of the porous early growth, the less compression strength your board has.

The reason most people use red oak is because it's easy to get and it works well.

If you can access some dense hickory or white oak you can go narrower.  The king of narrow bows is ipe.

If you can get Ipé it works well too.