The only recoil reducing stock I am aware of is the Knoxx stock, it is an ar15 type that is adjustable to length of pull. That is not to say there aren't any others out there. What you have in your pic is a speedfeed stock. A sidesaddle is usually attached to the receiver. I think I have seen some UTI or other stocks with a sidesaddle on the stock. It's been awhile since I looked for that stuff.
Look at the Mesa Tactical tube adaptors. Those use AR grips and stocks
"A strong body makes the mind strong. As to the species of exercises, I advise the gun. While this gives moderate exercise to the body, it gives boldness, enterprise and independence to the mind. Games played with the ball, and others of that nature, are too violent for the body and stamp no character on the mind. Let your gun therefore be your constant companion of your walks." Thomas Jefferson