Don't blame the rudder for that.
Turns steepen because the outside (top) wing travels faster than the inside (bottom) wing.
That is true but rudder has a much greater effect. Try it on Flight Sim. Yes I know it's not 100% aerodynamically correct but it's pretty good on steep turns (I'm using the Cessna 152 from the Flying Club package).
Keeping an eye on the ball is obviously the way to go but knowing what to expect in a manoeuvre that has already a high workload is a great help, in my opinion.
Some interesting contributions here though. Thanks!