You are correct in your assesment that the longer the club the flatter the swing plane, and the shorter the more upright.
Addressing your wrist wibble I interpret this as you are are snatching the club to far inside and rolling the clubface open too early on the backswing. A result of this is the right arm attaches to the right side too soon, and the club is on an extremely flat swing plane when this happens there is little if any chance of recovery.
Here is an excellent drill for you to do at home.
Hopefully you have a full length mirror at your home
Take your normal setup now note how the shaft creates an angle now put a peice of tape on the mirror that correlates with this put a peice of tape should be about 5 feet long so it goes over the top of your head.
Now swing the club back assuring that the club glides along this line this the correct swing plane for that club
Do this with all of your club
You will notice as you move down through the
clubs from driver to wedge that the angloe of that tape will steepen
Write back and let me know about your success
Jordy Scerbo
Teaching Professional