Thanks for the info, Grundtvig.
The tool-tip works, but takes 2 seconds to appear on my screen, plus one second to get the mouse to that point, times 15 documents open at once, equals up to 45 seconds just to figure out which document to click on, compared to the four seconds it would take if the shortened bars had the basic sense to show the file name. I think I'll go for the Window menu.
They really should have sorted out this obvious interface problem a long time ago, but I'm not sure who "they" are. Is this an Adobe choice or a Microsoft choice to do it this way?
The tabbed bar in FM8 is another possibility, although this takes up the same quantity of screen real estate that the shortened bars take up, and would have been unnecessary if the shortened bars showed the file name as expected in the first place.