What about if you select a window, press Alt-space, select Move from the menu by pressing M and then move the window with the arrow keys and press enter to accept the new position?
I had to learn this trick when a program I used frequently got a little too good at remembering window positions. I was using a laptop as my primary work computer, and at my desk had two extra monitors--but I also taught courses and gave off-site presentations regularly, and when hooking up to an unfamiliar projector, the default screen arrangements would often differ from my home base setup. The result was that sometimes when a connected projector was to the left of my laptop's screen, the program would open its dialog windows at the coordinates on the monitor to the right of my laptop--which of course was completely outside the visible area of both laptop and projector. For some reason, these dialog windows did not acknowledge the standard Windows key commands for moving and resizing windows. With nothing to click on, and none of my usual keyboard shortcuts working, I had to do some research to get it sorted.
Fortunately, the first time this happened to me was when I got back to my desk after a presentation, so I wasn't stuck in front of a crowd of clients trying to figure out how to access my hidden dialog windows. It did happen in front of clients a few times after that, but knowing the keyboard shortcuts meant I could fix the problem before anyone in the audience even noticed.