You are more or less right in you assumptions- More blades of the same area at the same pitch produce More thrust but also require more power. It's probably analogous to the gear ratio of a car- more blades equals higher gear and is more efficient at higher speeds (Hence may modern turbo-props have multiple bales), fewer blades equals faster acceleration (Needed for small aircraft using Short strips)
The reason, however, that you see more 3 or 4 blade retrofits in Europe is not because of this, however. More blades allows the blade Diameter to be reduce, reducing tip-speed for a given RPM. Much of the noise associated with prop aircraft is due to the prop tips operating at a high percentage of Mach 1.
More blades=smaller diameter= less tip speed= less noise. Necessary in noise conscious European cities.