OMG ... I found the problem.
Would you believe, the programmer window is
not actually being closed (shut down) at all -- but merely sent to the back, behind the main window, when I click OK the close the warning message!!! Further more, each time one clicks the button to bring up the programmer window, a NEW window is opened, with the same warning message. That new window also appears to close completely, as soon as the warning message is clicked away, but is in fact also merely sent behind the main window. GOOD GRIEF!! :-/
So this whole time -- this whole four plus freakin hours !!! -- has been all due to nothing more than a user interface design flaw!!
Clicking Window on the main Quartus menu (running maximized, fwiw) and selecting the existing Programmer window from there, gets us going just fine, with no other issues at all.
U N B E L I E V A B L E