Welcome
@85bittersweet to the forum and congrats on your new larger boat.
That your new boat backs differently is no surprise.
Look at the differences in the hulls
Catalina 30
View attachment 176546
Hunter 40
View attachment 176545
Of specific interest to your challenge in the location of the prop to the rudder. By locating the prop closer to the keep as water washes over the keel in the 30 it tends to reduce the tendency for the boat to change direction. Being "less" responsive more like a Cadillac than a sports car (the Hunter 40).
The Hunter puts the prop near the rudder and farther from the keel. So you loose the stabilization of the keel and get the more reactivity of the rudder. Small movements become exaggerated by the prop wash.
How I would deal with this design in the Hunter is to use small rudder changes and pulse the prop power. Get the boat going then pop the boat into neutral and coast using the small rudder changes to change direction as the boat coasts backwards.
Or you can go higher maintenance/cost and install a bow thruster and use it to counter the steering of the rudder direction changes. This would require a whole new set of skills but you could actually learn to push the boat sideways as you becoem proficient.
When you can, go out and practice the backing before you spend a lot of money on new props hoping for a magic solution that may never happen.