Thanks, Orac; quite a lot to think about, there.
The thing that “jumps out” of your post is the question: “…where does the energy come from?” You probably recall that I have been asking that question about gravity, in one guise or another, for some considerable time. I think I even proposed an answer once. I would like to come back to that when I have had time to follow your links.
In the meantime, I have taken the next step in my own (layman) thought process, and as usual, present it as though I were explaining it to someone else.
Let’s start with a 2D image. On a sheet of paper, draw a circular spot to represent the gravitating body. According to GR, this body causes spacetime around it to bend. At some distance from the body draw a smaller spot to represent an object approaching the body. It is in uniform motion, so draw a straight line to show what the trajectory of the object would be if the body were not there. Now draw a line to represent the trajectory of the object, with the body present, such that the object is diverted by the curvature of spacetime, but not captured. Next draw a line to show the object going into orbit around the body.
All this fits the spacetime curvature scenario quite well. There are a few questions that arise, but at first glance they may not be obvious. Before you part with your sketch, draw a line representing the trajectory of the object if it is travelling straight towards the centre of the body. In this case, the curvature of spacetime will influence the object equally from both sides – we are still working in 2D – so the line will remain straight, there is no change in direction. There is, however, a change in the objects progress towards the body. As gravity takes hold, the object will accelerate. This is where an alarm bell rings. Somewhere from the depths of memory a Newtonian equation begins to emerge. F = ma. Force equals mass times acceleration. Whichever way you rearrange this equation, the force is still there. What is that force, if it is not gravity?
