Here are some news- I adapted the upper V part of sync circuitry, connected composite sync in there and... it works! However the results with colors and brightness are even worse and also the screen is significantly moved to the left, I can see it is located too much to the left. I try to choose good resistors for my case and once again I can't do anything right. However I should move or delay the sync anyway in the first place. By the way, does moving sync affect the color information in any way??

Also, I had to get rid of that 0.03 cap and connect sync straightforward to resistors. This already isn't a good sign

 

There are two adjustments in the synch section and they seem to be setting the phase relationship between vertical and horizontal. synch. With the colors, does "worse" mean brighter or dimmer? At this point you have the gain of three input color channels and the output of the three signals to adjust to get the picture that you want,