Punches and top spin with Starters talk of "more roll" rather than "hold the greens". Try high shots => full & flop (which is more of a high pitch with Starters).
I remember being happy to hit any green with those at any place, using a lot of backspin, while not dreaming of short first putts :)
Practicing to hone your skills with such suboptimal equipment would be one way
An upgrade of material may be more effective for more fun. Any custom ball will improve your game - more with the wedges you have but also with the Starter part. Perhaps replace the Snake wedge with a Ping(?).
You've played quite a lot - almost 350 ranked rounds. I wonder why your average is so high - perhaps some thoughts of yours concerning the success of your shots might help? Also course management?
I don't like to use the stats against a player. Please allow me one blind guess and a hint regardless:
Is it that your short approaches are fairly unsuccessful? If so, consider to use only shots which land on the green from 30 yds in. Avoid chips unless you are sure to be successful hitting the green.
My 2 Pfennig