Turtle,
I've made a bunch of white ash self bows ....and it makes a great bow. I believe that if you back it with sinew, you will want to pick a design that favors an over-strong back. One example might be to trap the back before the sinew, or at the very least you will want to "crown" the back. Otherwise I feel that you run a risk of overpowering the belly.
Keep in mind that I use quartersawn wood, so take my experience for what ever it's worth to your project.
rich