1. Bright LEDs light even with nA current. I had a 5 meter LED stripe that some of the LEDs were ON while not connected to any power source!!! (Yeah, from static charge).

2. LEDs are not like lamps, so you cannot control them by a simple PWM idea. LEDs are current dependant devices so, you have to control them by current source and NOT by voltage as you do now.

My suggestion is not to bother with more resolution an try to control, by PWM, the current of the LEDs. Then you will have the exact same effect like simple filament lamps.

Ioannis