Why can't I resize a window's height to make it smaller when it is at full height?
Are you running any sort of third-party window management software? That's the only reason I can think of that this wouldn't work for you.

I can resize the height of my windows using the arrows on any visible edge, including the top and bottom of a max heigh window, and the diagonals. I tested this with the Dock hidden and visible, on the side and bottom, and with a window with a size exceeding that of the screen. Worked every time.

If you're not running any third-party software that might be interfering with window resizing for some reason, the only thing that comes to mind is that your mouse is very sensitive and you're moving it slightly before the click to resize actually registers.

You might also be interested in Moom. It's a pretty handy window manager that can do things like save preset window configurations for different display set ups, or do one-click window resizing to match a specific size in pixels (which you can bind to a hotkey). It's not a solution to not being able to manually resize, but if you're moving windows around different displays often, you may find it handy. Divvy is another popular app that does some of the same tasks, but I haven't tried it myself.