We went to the Munich Ausländerbehörde on an emergency appointment today and they told us we could not re-enter Germany with a Fiktionsbescheinigung under Abs. 3. We could if we had one under Abs. 4 (extension of an existing permit), but not if we have yet to receive our actual permits. (The Fiktionsbescheinigung is the document that says we've applied and they're working on the application; it allows us to stay legally in Germany).
I am not sure the Ausländerbehörde is correct on the entry requirements in light of the privilege granted to U.S. citizens under § 41 Abs. 1 AufenthV; I don't think the local Ausländerbehörde is responsible for administering or interpreting Germany's entry requirements for U.S. citizens. But we were not allowed to speak to anyone who actually knows the laws, and we seem to be at a dead end. The German and American embassies have just referred us back to the Munich Ausländerbehörde, and my inquiry to the German Federal Foreign Office has gone unanswered.
Without some official source confirming that we would be readmitted to Germany, we will have to abandon our trip to the U.S.