OK, I admit I know nothing about outboards but I cannot help myself
when it comes to inventing weird stuff, So............
Why not replace that whole heavy outboard on the transom with an engine
on the boat that turns a hydraulic pump that turns a hydraulic motor
hung from the transom. I know nothing about losses in the gear train
of an outboard vs those in such a hydraulic system but mounting would
sure be simpler as would be tilt and trim. The engine could be a
conventional lightweight 4 cycle without all the problems with making
it light enough for being transom hung. For that matter, maybe even a
small diesel could work instead of a gas engine to turn the hydraulic
pump thus making it all much more fuel efficient.
Of course, somebody has probably already thought of all of this.