If you think SynthID-Image can be easily defeated by adding entropy I invite you to give it a try.
I spent half a day messing around with it and I was very impressed by how robust it is. I couldn't get OpenAI to stop detecting their own SynthID without completely trashing the image.
What about asking LLM to re-draw the image from scratch? Or pass through AI editor?
Much prior art here, works against both Google and OpenAI's SynthID: https://github.com/0xROOTPLS/DeSynth