first off (to address the second issue first), i think by creating two planes and combining them you've made too much work for yourself, when you could have just created a plane that was as big as the other two combined and just deleted a face... that would ensure not only that the split polygon tool would move to verts easier (since it wasn't formerly two objects) but also that no vertex merging would be necessary.

as for the first issue, if ya gotta move verts, ya gotta move verts. there could be a way around it, but it would probably involve an alternate modeling technique from what you're currently doing. at the same time, you can always cut where you want and then snap the verts to the grid where you want them, and that doesn't take a long time at all. besides, isn't eyeballing it enough, or do you actually need to be exact?