Hmm no. I appreciate the lesson of general relativity, despite having been myself a physics olympiads finalist back in high school days and having read a gazillion of books about it, but I'm afraid that such lenghty and thoughtful comment is sligthly irrelevant.
You see, if we are to be rigorous, which you are forcing me to be now
, a G-Force is an acceleration that is measured against any einsteinian spacetime geodesic. A "gravitational" G-Force is exactly equal to an "acceleration" of a spaceship because it's exactly the same phenomena, i.e., you are being pulled (pushed?) over your own natural geodesic with a constant force. In the case of a gravity well, like the Earth, the 1G you are experiencing right now is due to the existence of a natural body that is stopping your own body from following its own natural geodesic line towards the center of the Earth. This "natural body" is exerting a constant force to maintain you in the "same" position every second. Likewise, in your spaceship, its hull is exerting a force against your own body, stopping you from going in the geodesic line your body wished to go to instead.
The phenomena is "equivalent" because it is "exactly the same". It matters not that it was Einstein or anyone else who figured this out, it's this "sameness" that makes it possible for us to quantify these different experiences in the exact same unit. You'll notice that in physics, when same units are applied, it's because it's the exact same phenomena that is occurring, even though in the middle of the derivations you get somewhat surprised at some so-called "equivalences".