Buying a new card will not solve your problem, getting two monitors/projectors that are the same native resolution will. Indeed clone/mirror mode only works when the resolutions are the same. You could enable GPU scaling called Letterboxing(or Maintain Aspect Ratio as its called in CCC) this will prevent the image from being stretched but will make black bars around the larger of the two screens to make up the difference in resolution.
Thanks. I'll try that.