I resolved issue with mode 1 where both channels working with 100% brightness.

I checked the current efficiency of the original power supply and it turned out that the current efficiency is 0.55A and the voltage Vout = 18.5V. Both channels require about 0.65A of current when lit with maximum brightness. I reduced the PWM fill value for modes 1, 2 and 3. Now the flickering effect does not occur. The whole thing looks pretty good. Pleasant warm color of light will certainly make long winter evenings more pleasant.

The device is now in the phase of long tests of 2-3 months. Perhaps in the meantime I will add some improvements to the software.