It's all in the lower unit and yes you can change the gears. It's alot
easier
to just change the lower unit, though. A good used lower unit can be found
for
about $300 or a rebuilt for about $500.

Well that makes sense.

My port outboard leg (whatever you call it, lower unit, the part the sticks
through the transom) has a label on it that says "counter rotating". I
suppose if it was the engine that ran backwards they would have put the
plate on there.

I suppose I could put a bit of thought into these things.