I figured out how to retrieve the window position, and the result was completely unexpected.
For values of n, this is the window position I got.
0: 2160, 135 (valid, center of non-primary monitor)
1: -1680, 135 (valid, center of non-primary monitor)
2: -720, 32792 (invalid)
3: -720, 32792 (invalid)
Not sure what's going on here, but it looks like something in Allegro overflowed.
Fortunately, I learned I can also use al_set_window_position to put the window in valid space, since it appears that 0, 0 will always be the upper-left coordinate of the primary monitor.
However, I'd also like to note here that al_get_window_position doesn't return the same value that you previously set it to in al_set_window_position. If I set the window position to 100, 100, and then retrieve the window position again, I get 103, 125. I'm using Allegro 5.0.7, so I'm not sure if this has been fixed in the latest release. (I think this was reported once already.)