I suspect when you snap back you are already in a state for WILD to occur more easily. See if doing something like this will help... once you snap back, you:

1. Relax your head and allow the back of it to sink into the pillow. You can even force it a little bit.

2 Do a few more relaxed cycle.
3. Very delicately release the stone in your hand, try not engaging your muscles.
4. Assuming you've done step 3 successfully you direct attention to your nose. You should feel some pressure on it.

5. Again, without involving your muscles you raise your hand and move it toward your nose. Don't worry if it seems like you are gliding through and rubbing against the blanket.

6. Pinch your nose and see if you can breathe. If you can indeed breathe you are in a dream and by this time you have directed your focus into it (instead of reality.)

7. Gently pull yourself up toward the direction of your hand and you should be in a WILD/OBE whatever you prefer to call it.

If you fail at step 3, say, it's impossible for you to control your hand without using muscles then you can repeat step 1 and 2 then try again. Or of course, just go back to sleep.

Moving your hand without muscle sounds like something difficult to do. It indeed is when you're fully awake. However, in that delicate SSILD-induced waking state it is not at all impossible. For me and many others, it is even possible to accomplish that after we've physically moved. You can trust SSILD has conditioned your mind and body properly for that to happen. Hope this helps! Your experiment is very interesting! Good work! :)