Based on your statement ‘business meeting’, I assume this was a paid ticket and not an award. Award tickets are tricky, but on a paid business class ticket as a 1K, it should be absolutely no problem to get a rebooking on DL/AA, in particular if the issue was ‘controllable’ on UA’s end. It has been a while to have this issue, but whenever I encountered it I always resolved it in the lounge rather than on the phone. Have been re-routed numerous times on e.g. DL direct BOS-LHR when BOS-EWR-LHR became impossible. Never any pushback.