As far as I can tell my mental map of the universe works pretty well,

Do you regularly encounter situations where your map of GR is tested?

I'm putting this out there to clarify my understanding and get comments on it, so I accept your comment, but how would YOU phrase your answer to the question of how gravity works, in a better, non-Fake-Explanation way?

Or, alternatively, how would you rewrite my answer in a better, non-Fake-Explanation way?

Sure:

Question: "Where the frak does gravity get its power source?"

Newtonian Answer: "It's not really a source like a battery or a motor. What you're seeing is the changing of energy from one kind to another. The fact that masses [creates a gravitational field] creates a way for the positions of potential energy to be changed into the motions of kinetic energy. ...

GR Answer: "This question is related to a major unsolved problem in general relativity.