Hooking the string, as you have stated, in the first joint of the fingers is considered a deep hook already. You can go further...I hook the string, shooting 3-finger split, so that the string is placed between the 1st and 2nd joint of my middle finger, is in the 1st joint of my ring finger, and the index finger just rests on the arrow shaft to keep it in place. If this doesn't make sense I can post a pic later today after work. It may sound counter intuitive, but I get a much cleaner release the deeper I hook the string. YMMV...
Bill-