Salvaging your shield, my recommendations, based on the picture in my mind as you described it (which may not be reality)
1) Remove the handle you have
2) Cut out a circle in the center for your hand. The easiest way to do this is a with a 6 inch hole saw (~$25) and a quality power drill. The second best way to cut a circular hole is with a jig saw. The jig saw may give you trouble if you have two layers of foam on the back of the shield already because the saw may not cut the ply wood as it can bounce on the foam. If so you will have to rip off the backing foam.
3) Don't worry about cutting through the front foam on your shield. In fact you want to cut it out so there is a hole all the way through (gives room for your knuckles).
4) Cut a slot in your backing foam and get a new handle in the form of a piece of wood (like a 1 x 2). Round the handle a bit where your hand will grip it. Also put tape around only the grip. Finally glue and sc-rew it directly to the plywood.
5) On the face of your shield where you have a large hole, place an 8 inch circle of 1/2 inch blue foam over the hole. Glue it around the edge and then tape it down. The result is a only 1/2 inch of foam between your fist and the front of the shield.
6) If your face foam is deep enough this sometimes is sufficient on its own. But if your fist is right there you will want to cut a foam ball in half and place it over the center as a shield boss. I recommend making a cover first. Then sewing the 1/2 ball into the cover so that it is at the center of the shield.
(Something like:
http://www.andrewwelton.com/static/olre ... G_1392.JPG)