Yesterday attempt to play with component values was the failure.
Each power rail has 50 Ohm resistor and SMD coil in series. 50 Ohm resistor is more important for noise reduction than coil, however causes loss of 0.35-0.6 V when in idle state.
Removing 50 Ohms causes around twice higher output noise. No change in coil size, from available managed to help (up to 4.7 uH) Today maybe more experiments.