Ok, I was able to try a LumaFix 64 with a 6569R5 (I also have a 6569R3 and an 8565R2) on my C64R MK2. Using S-video - without LumaFix 64, the output is bad. At least the text is more readable but I have color artifacts (like repetitive vertical rainbows). Since my smartphone tends to bluish the picture on the screen, I'm borrowing another picture from C128 to show a similar effect:
So I tried the LumaFix 64 and was able to reduce vertical artifacts with AEC and PHI0 tweaking. But nothing regarding with CHR. So with or without LumaFix 64, I have those disgusting rainbows. Maybe it is an issue with my screen but it is clear that S-video output added to C64R MK2 is not that great.