Firstly let's consider a single LED circuit
Specified forward voltage is 3.0 to 3.2 and rated current is 20mA
Using the lower voltage and assuming a 5volt supply, we need to drop 2 volts across the current control resistor (R)
By using the lower forward voltage we ensure the current control resistor is sized for maximum current control dropped voltage, hence LED is never over-driven.
R = 2/.02 = 100 ohms (so you got that part correct - well done)
My suggestion of using the PWM driven FET still stands since the FET is not used as a voltage dropping device; rather it is a switch which turns the LEDs on or off at the PWM frequency. If the LED is switched on for say 1mS and off for 1 mS continuously it will appear dimmer than it would if it was permanently energised. Let's say half as bright, though I'm sure I'll soon get told that eye response is non-linear - but it will appear dimmer. Maybe someone will advise on what the perceived dimness tabulation is for PWM ranging from 0% to 100%
Because the FET is switching circuits, and has a very low ON resistance (typically <0.05 ohms), a single FET can be used to control all your LEDs.
jack