Just been experimenting with the split tool a bit. Perhaps something you should be aware of, check my picture below (if only I knew how to paste images -inside- of these text thingies, anyways). If I would want to create the yellow or blue new edge with the tool, I would simply click on the edge above or below it to start there ( I've put a yellow and blue line next to the edges you then select when you wanted the with dots marked new edges . That should pose no prob, however, if you would want to create a new edge left of the blue on, under another edge ( left-under the red arrow), I would have to select one of the 2 edges bordering that face. It would be wrong (and the tool wouldn't work), if I selected the edge with the red line next to it. I hope this makes any sence, and if it does that this solves your problem, but in short words:
Around the face you want to create an edge in, click only on edges that are directely to it, as it only works then.
PS: I'm quite sleepy right now, and I guess this doesn't answer your problem one bit, heh, it's more as a memo to myself, telling me not to do that..... If this helps anyone here ya go, if not, sorry for filling up the limited amount of bytes on SM by being so vague