Export again and look for the ProRes 4444 XQ codec (it's the best quality of all of them.) If you don't have it, then you haven't gotten the latest update of prores codecs. Check the Motion (menu) > Download Additional Content ... If that's active, then the codecs should be waiting for you. It should NOT (edit) matter which "level" of ProRes you use, the quality should be good enough to keep the banding from occurring (even PR Proxy.)
If you do have it, then check the Render settings of the Export. In the Export dialog, there is a Render tab. Most of the options say to Use Canvas Settings, but that can be overridden. Try setting the Render Quality setting to Best.
Hope that helps.