I hate generlaziations because someone always comes up with an example that shows your wrong. but generally smaller diameter, higher pitched props are for speed because they have less drag. Look at say a pre-war supermarine to see what I mean. Longer props will develop higher static thrust, extreme example is helicopter blades, there long because they have to be to develop enough lift.
Your case is a perfect sales pitch for a constant speed prop, but those cost money and add weight.
Oh yeah I forgot, generally speaking three blade props will out climb two blade (more bite just like a longer prop), but are slower in cruise (more drag, just like a long prop) are are heavier to boot.
I'm putting a Hartzell scimitar on my M-6/235, I'm hoping that the scimitar blade design will help keep me from losing too much in cruise, but I feel that I will have to lose some, just so long as I get a little better short field I won't mind.
I guess that any prop is some sort of compromise, you just have to determine what you want it to do best or pick a prop that does everything OK, but nothing well.