After years of resisting, I have just started to use a shooting jacket.
They dampen the felt heart rate a lot and also because of their stiffness, they give extra support to the arms and upper body.
However, as Ratinator says, they are an aid to good technique, so if you can borrow one, try it, you will see less wobble through the scope, but you still need stability and good technique.
You mention a higher scope position. That is pretty common over here these days, but will require you to raise the cheek piece, this is easier on some rifles than others, and some, like the EV2 and FTP900 have parts available from the factory.
All of this is part and parcel of getting the fit of the rifle right, just get one thing right at a time and you will find stability and comfort improving along with your scores.
"I'm your huckleberry, that's just my game"