Edit: I thought I could do it but it did not work - though I think I was close.
This isn't in the scope of gridmove, because gridmove always resises the window.
But this really isn't very hard to do as an ahk app, i'm sure some of the other ahk coders here could easily do it.-jgpaiva
Sorry for resurrecting an old thread, especially since I think you already have an answer, but I think GridMove could almost do this.
It could be another feature If this gird worked:
[Groups]
NumberOfGroups = 1
[1]
TriggerTop = [Monitor1Top] + [Monitor1Height] /4
TriggerBottom = [Monitor1Top] + [Monitor1Height] *3/4
TriggerLeft = [Monitor1Left] + [Monitor1Width] /4
TriggerRight = [Monitor1Left] + [Monitor1Width] *3/4
GridTop = [Monitor1Top] + [Monitor1Height] /2 - WindowHeight /2
GridBottom = [Monitor1Top] + [Monitor1Height] /2 + WindowHeight /2
GridLeft = [Monitor1Left] + [Monitor1Width] /2 - WindowWidth /2
GridRight = [Monitor1Left] + [Monitor1Width] /2 + WindowWidth /2
The issue as I see it is that GridMove doesn't do math on "WindowWidth" or "WindowHeight". Of course I have no idea how much it would take to make that work. I also don't know how many people would want this feature.