But I can't see why you would want to. Why go to the considerable expense, given all the complex double curvature involved, of building a butty stern, and then motorise it. A motorised butty is never as efficient as a boat properly designed as a motor boat. And if you put a counter on it, surely you are not even going to see the butty stern. Once it's properly ballasted you just see the counter. Or are you suggesting you still retain the butty shape ellum and tiller bar? That would probably be even more bizarre. There is presumably something I am not understanding about your concept.
Is that prop and cowl fixed, so it only gives thrust directly backwards, or does it move so you get your steering in that way. There does not look to be a lot of rudder left to redirect thrust. We did a couple of hydraulic drive conversions in the 80s, one to a River Lee size lighter owned by Gren Middleton and used as a puppet theatre. We mounted the prop in the rudder itself so it acted as an outdrive. The lighter had about a foot of concrete in the bottom to serve as floor and for stability so was very heavy, but it steered magnificently, even in reverse. We powered it with a 2.2 BMC mounted crosswise right in the very stern.
Actually I take back my comment about a motorised butty never being as steerable as a motorboat, as it could be done. But I'd still ask why.