Since Mooney's sit low, does this mean prop clearance is an issue?
Hence a short prop, hence a fat blade?

You probably have it right.

From my observations, prop design seems to be more of an art than a science.
This topic is very confusing.

An interesting aspect of prop design is not only the chord shape but also
the number of blades. People generally think that more horsepower requires
more blades. But witness the Piper Malibu's two-blader (350 hp) and the
Piper Turbo Seminole's three-blader (180 hp).

Mooney's Ovation was initially sold with a three blade prop but later
changed to a two blade (Ovation 2) and it picked up 8 knots of airspeed.
Evidently this was due to the efficiency gains of the two blade, the same
reason it was chosen for the Malibu.

I believe three bladers are preferred for their reduced vibration, quiter
operation, greater low speed thrust, and appearance. Chord design probably
is the main factor in determining the efficiency of the prop regardless of
the number of blades.

Frankie