OKAY, this isn't the issue afterall.
For some reason the upgrade to Unity 5.6.1p4 messed up something in our UI causing it to destroy the menu manager. We're still working on this bug, but consider the above issue closed.
Aha. There's an issue fix in Unity 5.6.1p2
https://issuetracker.unity3d.com/issues/build-dontdestroyonload-object-is-destroyed-if-scene-is-changed-while-its-inactive-and-then-that-object-is-activated
BUT, it seems to have had the OPPOSITE effect …