Any question answered...

Obviously it's super easy to leave the paint section - minimise/close /open some thing else/etc.

Resize the window to exceed the visible area, using the keyboard? I used to do this trick on Win3.1 I think. Step by step:

• First manually maximise the upper part of the window, by resizing it to fit the top part of the screen
  
• Use ALT+Spacebar to open "shortcut menu" (internet search tells me this is the shortcut) It might also be possible to access it with a right-click in the taskbar, not sure
  
• Select the "Move" option (I always did this with arrow keys and Enter)
  
• Using keyboard arrow keys move the top of it offscreen slightly (up up up) so the app title bar is not visible any more, and window decoration buttons are inaccessible. So no more minimise/maximise/close buttons nor the app icon/shortcut menu (the one on the top left)
  
• Hit the Enter key to finish moving
  
• Using the mouse, resize the bottom part of the window to cover the remaining display area
  
• Auto-hide taskbar? (Maybe relocate it to the right side of the screen or the top, so it's less in the way)