Propping up my Assumptions
I have always understood that the limiting factor, within limits, is the tip clearance to the hull. One company web site calls for 15% of the prop diameter. Most of us strive for about 1.5" of clearance. This is said to reduce the vibration from water hammer against the hull, each passage of a blade.
When spec-ing out a prop, I would then try to balance the increasing blade area as the diameter increases with a proportional decrease in pitch. That's my intuition, and it might be wrong.
After owning our boat for over 2 decades, and using several different props on it, we have "evolved" to the present sizing and we are the fastest under power that we have ever been. There seems to be some gray area in selecting the right prop, although most of the factors are indeed science-based.
I suspect that the shape of the nearby hull and the aft shape are important too.
(The best prop engineers and installers may have a Dark Wizard working in their technical department...)
If you (using google) search this site for prop information, there is a lot of discussion of what works. While it's anecdotal, it is sincere and first hand.
Best,
Loren