Not sure what can be causing this, as the sync pulse seems to be amplified a bit, but not as much as the burst, so there might be some filtering going on, though I’ve simulated the send subcircuit and everything looks fine.
When it comes to the color shift, it is probably because of the filtering/delay induced by the components in the path of the video return. A full hue cycle in NTSC is a 360° phase shift of the color subcarrier, so that’s about 280ns of delay, then to go from Red to Magenta, it asks for a 60° phase shift, which is about 46ns. Usually, a hue compensation circuit is used to adjust the phase of the color burst so it matches the processed video, as unless the processing part ends up with exactly 360° phase shift, there will always be a little bit of delay. It would be even more useful to have a hue adjustment on circuits such as Sync-ope, because there can be anything in the send-return loop, and each device in the chain will have a different delay.
That’s something I’m looking to implement on my stabilization module, there is some simple transistor based phase shifters, like in this Vidicraft Proc Amp (which is NTSC):
http://soundexcellence.com/old_products/ProcAmp_5-Schematic.pdf (the Chroma Phase Preset and Chroma Phase on the right part of the schematic)
And seems like the circuit inspired people from Progetto Elektor for a PAL version, though there is no Chroma Phase Preset trimmer:
https://github.com/Syntonie/videomagazines/blob/main/Progetto%20Elektor%20(Italy)/ProgettoElektor_1987_07-08%20Color%20Processor.pdf (Tint potentiometer at the right of the schematic)