An overhead projector is a lightbox with a stage that transparencies lay on, where the light is then passed to an overarm lens that then focuses it on a screen. I think you mean a front projector, either an LCD of a DLP? I apologize if I am wrong here.
For my home theater, I've used
A2Z Cables. If they don't have a cable that will work, they can custom make one. I had them custom-make a component-to-RGB breakout cable, and the quality was superb.
Best Regards,
Dave