Actually, I think that when you are pulling up your anchor, it is OK to swap the rode from the bow to the stern. If the anchor sticks, you will just stop tight. I don't think you can sink your boat in this manner. The worst that can happen is the stern comes down, but since you are (presumably) heading upstream, that's OK. The swap from bow to stern could be tricky, though. If for some reason you have already tied off to the stern, then you lose power or get spun around, things could get ugly. A sharp knife is the tool of choice at that point .

Nothing can save you, however, if you get the rode wrapped around the prop -- you can't get it loose or cut it without hanging your arse off the back of the boat, it likely will stall the motor, and now you are at the mercy of the river. Getting the rode wrapped up in the prop is a lot less likely when it is tied off of a stern cleat.