this would REQUIRE a nazi victory or negotiated peace.
I wouldn't go that far. Even a battlefield negotiated surrender they could probably still retain Austria, just likely not under FDR, who was more convinced of punishing Germany and all Germans collectively then even Churchill or hell even Stalin... and that says a hell of alot considering one had his cities bombed by the Germans killing tens of thousands of civilians and the other had his people killed by the millions by Germans and their allies, not that he cared about that, but he was deeply embarrassed by his early defeats.