I think what you'd want to do is press insert to go into Pivot mode where you are able to move your object's pivot point. Snap your pivot to one of the vertices you want the mirror to flush with. Press Insert again, to return to normal mode, duplicate your object, put -1 in whichever Scale direction you need, and it should mirror around that pivot point, which, if placed correctly, shouldn't leave any gaps...

Hope that works for ya.