Paul: a very nice summary!
There are other approaches to QGD. the Wikipedia article on quantum gravity lists a couple of dozen or so.
Stephen Wolfram and I have long thought that the universe may be a cellular automaton with as-yet unknown rules. A recent development by Wolfram posits that the fundamental quantities in the cellular automaton may not be occupancy (as in the classic Game of Life) but graphs. The rules convert a parent graph into another for its child. https://www.wolframphysics.org/technical-introduction/ contains a simple but lengthy exposition of his ideas. https://www.wolframphysics.org/ itself gives links to a wide variety of related topics.