See the nastiness below (click on it for a more detailed view):

I'm just about to give up on it, and turn the shading off for the desk, when I had one more try, fiddling with the lighting options. And lo and behold, guess what happens? I fixed it!!!

Woo hoo!! But what was it that actually fixed the shadows? One single click of the mouse. An adjustment by a mere -1:
I then went and explored iClone Help, where it simply says:
Shadow Bias Adjustment
This function helps to correct some shadow displacement errors caused by extreme shadow angles.
Well, duh...
If only I'd gone looking at the Help earlier... oh well, at least I went by my own tried and true rule, "If it doesn't work at first, keep clicking!"
Now back to work, Mr Trek...!