The good news is you're not a "sinker". Reading your descriptions, most of the problem is position, balance, and timing. A good test to see if you are in correct position is do Superman to (good) Skate - then roll chin to shoulder and see if you get air. If you find only water and no air, position and balance are off.
Any one or combination of the following will prevent you from getting air in Skate: 1. lifting head, 2. tension in neck pushing head down, 3. over-rotation, shoulders are stacked, 4. recovery elbow is lifting above the surface (causes arched back and hips sink). We often refer to this as the "chicken wing". Make sure recovery arm (non skating arm) is molded to the front of body and not wrapped around outside of hip.
If you can, have someone take an above surface video (cam phone is fine) of at least 8-12 strokes and getting at least one breath in whole-stroke, breathing toward the the person filming. And another video of the Skate rolling chin to shoulder breath - and post here.