One more point about using a router for cutting. Remember that the bit is not always going to be centered in the base plate.
I'm highly interested in what brand and model of router you have, as I have owned 4 different routers, and each is dead nuts center. I've had a Craftsman, Milwaukee, Porter-Cable, and now a Ryobi with 3 different base attachments, all centered.
So to compensate for this you just have to make sure that you are always running the same spot on the base plate against your straight edge.
since the base plate is almost ALWAYS circular, it would be highly improbable that you're going to be that precise. I've never attempted to do this, and have never, meaning not once, had an issue with this.
I have also made a special base plate that has a straight edge on one side instead of being circular.
I believe Fein, DeWalt, and Milwaukee either come standard with this type of base, or have it as an option. There may be others, but those are a few that come to mind.
I'm very interested to know what make/model you have, as your experience seems to be directly contrary to mine.