If Meyer-Werft ended up with the contract I foresee several problems. STX has the build experience for Oasis-class, plus any proprietary construction tooling/methods involved. This means that M-F would not have the benefit of the construction efficiencies STX would have and thus the 3rd ship could cost more to build. Now, I imagine STX could have a sub-contractor relationship through Meyer-Werft, and thus have a hand in it at least from an engineering support aspect, but again that would come at a price.
There is a reason all U.S. Navy aircraft carriers are built solely by Newport News Shipbuilding (or whatever they call themselves today...I think it is Grumman something).