There could be a broken pin inside the A1200 that connects the chromanance to the composite output. The logical diagnostics' next step would be to either connect your Amiga to an RGB analog monitor. Since you've tried other TVs we know that the problem is in your Amiga so there wouldn't be any point in trying a different Amiga on your TV. My suggestion would be to try to find a cheap monitor like a Commodore 1084S with the Amiga cabling, to find another A1200, or get one of those TV adapters for the A500 and use it on your A1200. Sorry I didn't have better news.