Animal hides have stretch. Across the hide from side to side stretches the most. Lengthwise, from head to tail, stretches the least. The best orientation for bow backing is from head to tail. You only have to cover the working portion of the limb anyway. If it is still too short you can splice it mid limb and secure the splice with a wrap. A similar splice and wrap on the other limb will even out the decorative effect.
I usually don't add rawhide or snake skin backings all the way to the tip. I leave the last 6" or so bare and wrap where the backing ends.