Thank you, Shawn. I was about to write a long rebuttal of your suggestion (because you were offering me the shortcut I already had in place), but I was humble enough to try the second part of your suggestion by moving it. What I discovered is that the same strategy we used to used with XP is the ONLY way it now works in Win 7.
Take that shortcut to "Administrative Tools" in it's default location at "C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Administrative Tools"
and, as you suggest, drag-and-drop it to the place you want it to appear. (I'd tried cut-and-paste, in the past, to no success; apparently is the Dragon-Drop that does the trick.)
Apparently, for Control Panel objects, that's the only proper way to move them, and it causes their references to be updated by implication. So, it's now working, and it worked through a full, cold reboot, and irrespective of whether the Control Panel is access as "menu" or "link."