Can I dim my LEDs even more?
My goal is to dim those LEDs to the maximum point

The eye can detect a massive range of luminance (x axis) with a really moderate change of brightness (y axis): -

(source: telescope-optics.net)
For a change in luminance of over a hundred dB the eye can still detect light. The luminance emitted is proportional to power supplied to the LED so if you can only change the duty cycle by 255:1 that's a change in power of 24 dB. To increase the range of brightness you need a much wider control of duty cycle or the ability to modulate the current taken by the LED when activated by the PWM signal.

Can I somehow decrease pulse width even more from the software?

Nobody but you can answer this.