Now I understand your thinking charge, but the effect in this topic would not really be any consideration in prop design.
So now a few basic prop principles.
On all, possibly almost all, WWII fighter had constant speeds prop. This works simply by increasing or decreasing blade angle to maintain the same RPM at almost all flying speeds until the prop is mechanically unable to increase or decrease pitch. In speeds from stalls to well above max level speed the prop will maintain the same RPM.
2nd it is always preferred to make a longer prop then a shorter one for efficiencies sake. But mechanical limits come into play very quickly. Tip speed is normally just compensated for in the gear box of the prop. Most WWII gear ratio's were 1.5 - 2.0. A 109G10 is 1.6 a P51D is slightly over 2.0.
In almost all cases prop length is simply determined simply by ground clearance. After which other methods must be used to increase thrust.
At slower speeds the pitch will continue to increase until the RPM setting is reached. This has the effect of turning the prop past stall AOA of the prop, so it is wasting lots of power in drag to keep the rpm down. As you increase speed the planes speed with lower the AOA on the prop, and it will gain efficiency as it's AOA starts coming out of the stall regime.
Now once you have made the prop as long as possible with out striking the ground, you need to do something to absorb the power. The choices are add more blades, or add more area to the blades. Making the blades wider changes there aspect ratio and increases induced drag just like it does on a wing.
Adding Blades also decreases efficiency because of disruptive air flow from the previous blades. These effects decrease efficiency at high speeds, but increase the efficiency in the climb speed ranges.
But none of these choices and trade offs have an effect on how much thrust is produced in the lift direction, that is simple trigonometry. Also when doing lift calcs you must also take climb angle into account for required lift. If a plane is traveling straight up or straight down zero lift is required. So the total lift required (including thrust from the prop in the lift dirction) for non turning flight is the cos(ClimbAngle) * Weight.
HiTech