Artificial Monitor Center

I have a fairly nice computer system at work, with two monitors side-by-side. I set up the screen display to use all of it as one continuous screen, with of course the caveat that the continuity is broken by the monitor bezels (the physical edges of the monitors). I like it that way for several reasons (nice large spectacular "wallpaper" background pictures just look better on a big screen, for example).

The exact center of this double-wide screen is, of course, right there in the middle where the monitor bezels are. That means for any window that by-default pops up in the center of the screen, half of it is on the left monitor and half of it is on the right monitor. All the data being displayed is there (the bezels are not like an old-fashioned window where wood surrounds individual panes of glass and the pieces of wood can hide things behind them), but the discontinuity in the middle of the popped-up window is annoying.

So I'd like to be able to specify to the Operating System that I'd like some particular point on one of my two monitors to become the default "artificial center" where all pop-up windows will appear.