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First let me say that I’ve been using term “blockworld” (BW) for years and was only this year told by my philosopher of science colleague that it’s now “block universe.” Since I’m speaking with a fellow physicist, I’m going to revert to BW 🙂
I received my PhD in general relativity (GR) and have taught it many times, so I perhaps take for granted that many (most?) physicists have no formal training in GR. But, what you said is right on the money – GR assumes a spacetime manifold with a certain topological structure upon which one associates a metric and stress-energy tensor (SET). Einstein’s equations then provide a “consistency criterion” that the metric and SET must jointly satisfy. Accordingly, there are many such “self-consistent” combinations of metric and SET, while physics only uses a few. Special relativity (SR) then applies in the locally flat (M4) regions of the curved spacetime manifold of GR (so that’s where you can apply your Lorentz transformations).
SR is where one encounters the relativity of simultaneity (RoS), although it can also be introduced to curved GR spacetimes that allow for global foliations (not all do). [In the case of curved spacetime however, it may be that observers on a surface of simultaneity are moving with respect to each other, e.g., surfaces of homogeneity in big bang cosmology models. And, such observers occupy different M4 frames, so SR can’t be used between them.] It’s RoS that implies (but not entails) BW, as I explain in my handout attached above (SR-Example-Phy200.pdf). That example is written for intro physics students, so if you read it carefully, I’m sure you’ll understand how RoS implies BW. If you want a layperson’s intro to BW, just watch the 11-min segment from 17:55 to 28:55 of https://www.youtube.com/watch?v=NcOBtnU-zSA
There are at least three general ways people accommodate the stochastic nature of QM in a BW, two are retro-time-evolved stories told from the perspective of an observer inside the BW (“dynamical” approach, Price’s “perspectival view”) and the other is an adynamical approach per a view “outside” of 4D spacetime using a “global constraint” of some sort. Examples of the two dynamical approaches are Cramer’s Transactional Interpretation http://arxiv.org/pdf/1503.00039 that invokes “pseudo-time” processes (processes in a time that isn’t housed in spacetime, whatever that means) and Kastner’s Possibilist TI http://www.ijqf.org/forums/topic/possibilist-transactional-interpretation which modifies TI so that the processes refer to proper time along observers’ worldlines, i.e., a time that actually resides in spacetime. RBW with its adynamical global constraint is an example of the adynamical approach, as is Price’s Helsinki (toy) model. I’m not sure how to classify the Two State Vector Formalism, they talk as if they’re using a “pseudo-time” a la Cramer, but Aharonov has proposed a different notion of time that he’s hoping is more along the lines of Becoming rather than BW http://arxiv.org/pdf/1305.1615v1.pdf.
Let me know if you require further clarification!