I remember that bow, DoubleW! It was pretty flashy! And so were the arrows.
Since purpleheart has a tendency to fret, make sure you go long in the limbs like ryoonn says. I've always thought backing it with a thin slice of maple would be a great contrast. With a simple oil finish you will have a strong contrast between the colors of the two woods.
You may want to consider using a spar varnish with UV inhibitors as your final coat of finish. As I understand it, purpleheart, like osage, will darken when sunlight has it's way with it. Purpleheart will turn brown eventually.
And as always, post pics of the process and the finished bows. Many of us can't read, we can only look at the pretty pitchers!