Chuck
As you'll know from my profile - I'm a low hours PPL. I don't pretend to be anything different. No willie waving required!
However, I understand that certainly on the newest Airbus aircraft (A380) you can command a side slip angle using the rudder pedals, with help from three vanes mounted on the nose which calculate the sideslip angle. The system will automatically put in the correct bank angle to maintain the heading. At least one article has been written which includes testing this during a simulated approach.
Not quite sure what alpha floor has got to do with it. If you hit alpha floor protection you are going around...
However, back on topic I quoted the airbus doc as it includes graphs of bank angle vs crab angle for different crosswind speeds with geometry limitations. The numbers aren't going to work for your average PA28 but it shows how these relate to approach speed and how you can reduce extremes of bank or crab angle by combining them.