I wouldn't waste your money and NOT use those targets. Have you considered using them for shotgun use only? Invest in better targets for more precise point of impact and point of aim.
I see this all the time at Appleseed events. It's Step 3 of the 6 Steps that you're struggling with. Step 3 is the Respiratory Pause. For most of us there is a small window (a few seconds max) at the bottom of our breathing cycle that is ideal for squeezing off a round with minimal shaking. You seem to be one of the rare cases. What you need to do is focus on holding at the bottom of your breathing cycle for a bit longer (5 minutes minimum). It will be difficult. Things will start to get fuzzy. Keeping holding that breath. When things go totally dark, you're almost there. Just hold your breath a little longer and you'll finally see a bright light. Once your eyes have adjusted to the bright light you should be able to see everything with a new clarity and your shakes should be cured.*
*Please note, the above statement is neither approved nor endorsed by Project Appleseed, myself, or any sane person.