Jeff Mingay,
Norman's off-season tournament you saw is held at Tiburon in Naples, connected to a very nice Ritz-Carlton. The original 27 holes are a blast in my estimation--not a blade of rough, enormous fairways, no mounding and no contrived earth shapes, fast surfaces (depending on the month), lots of possible playing angles, invasive sod-wall bunkering and sleek, crowned greens. I think it's a very intuitive use of an absolute flat, wetlands infringed property. The nine they added a few years ago, however, seemed forced.
My issues with the Norman-designed courses I've seen is that there's too much of the above (including formal white sugar sand bunkers and crushed coquina waste bunkers/cartpaths) and it's often not suited to the sites they have. I'd like to see the firm react more to the land rather than apply their consistent formula. That said, most of what I've seen has been in the southeast on not always the greatest sites:
Tiburon--Naples
Grande Lakes--Orlando
Champions Gate--Orlando
Shark's Tooth--Panama City Beach
The River Club--Duluth, GA
Sugarloaf--Duluth, GA
Doonbeg