Even then, with as you said, on board propulsion needed to accelerate the craft, if it was a craft, we would need to have knowledge of the propulsion unit, with history of, directions and degrees of thrust etc, to be anywhere close to determining where it might have came from. Without that, we can have no real knowledge of where it might have come from, even with all the other things you mentioned known, this would be a critical unknown which removes all possibilities of being able to deduce possible source locations, no?