There was a boat as you describe last week moored on the North Oxford facing south, moored up in a line of boats. The outboard was on the left side of the rudder. I'm sure this will be the boat you are after, but I can't remember exactly where it was. I'm sure we passed it last Thursday, which would put it between Newbold and Braunston, and I'm pretty sure it was early in the day, so nearer Newbold. I'll keep racking my brains for the exact location, but from what you have said, it seems to be in the same area.
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Brain in gear (possibly)...........Does 'Lichfield' ring a bell ???????????????