You might also investigate a round trip ticket from Europe back to the US with a throwaway “return” leg. That has lately seemed to price out quite a bit less than originating in the US. If that works, you could do awards for the outbound (US-Europe) and then pay for the return. I’ve set up a few back-to-back trips next year using this method with the outbound a single award and then just daisy-chaining the subsequent flights across trips.