Thanks to everyone for your replies.
Yes, I calibrate my display monthly with an X-Rite ColorMunki with i1Studio software. I usually use these settings: D65 white point and 100 cd/m2, though I have tried other profiles (e.g. D55). I also create my own ICC Profiles (with the same X-Rite tool) to use with my Epson P800 printer.
I understand the difference between images on a screen (projected light) and prints (reflected light), and thus I also understand the importance of the type and color of the light under which prints are viewed (I have a pair of lighting fixtures with 2500 lumens, daylight 5000K bulbs). Indeed I have found that if I view my prints outdoors (in the shade on a sunny day) they look much, much better.
My frustration is that I cannot expect to be able to show my prints to people under those ideal conditions. However, it sounds like I will have to live with that frustration.
So, the consensus is that there is little reason to believe that switching from my iMac display to a NEC, Eizo, or Benq display will make much difference?
Steve