Paradox, noun: a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.
The Twin Paradox is most certainly that.
Before bringing general relativity (GR) into the mix, it's important to understand exactly what the paradox is, as it is much more than just an asymmetry between the twins' world-lines.
In the simplest formulation of the problem (and since it's a thought experiment: why complicate it?), twin A stays at home in his stationary pool--training, while twin B sets off running at near the speed of light. (I'm using triathletes because of the OP's profile).
During the marathon journey, twin A sees twin B aging more slowly. Meanwhile twin B sees twin A aging more slowly. This is already a paradox for some, but easily resolved with the Lorentz transformation.
Now comes the all important "transition" portion of the training: run-to-bike. Twin B is good, he can do it in 0 seconds. Just like that he is headed home on his Zipp, at near the speed of light. Note that twin A looks out and agrees: wow: that exchange took 0 seconds--in fact all observers agree, it was instantaneous.
On the ride home, twin A sees twin B aging more slowly, and vice versa; yet when they meet up, twin B is much younger.
Now that is a paradox: if they always see the other aging more slowly:
(1) how can that be in any case?
(2) how come twin B aged less?
Well, people say it's an asymmetry, or there's acceleration. All true: but the elapsed transition time was 0 seconds in each frame. How can zero seconds in each frame account for years of difference between the frames?
The resolution comes in the relativity of simultaneity: when twin B transitions, his definition of "now" on Earth makes a great leap forward--years. Since all this is occurring outside his light cone, it has no effect on him--he turns around and "computes" that far outside his light cone, his brother is now much older, and when he gets home, he discovers he was right.
In summary: A and B always see each other aging more slowly. When B turns around, A says his clock advances 0 seconds, and he says B's clock advances 0 seconds (though B is far outside his light cone, and he only learns of this later). Meanwhile B says his clock advances zero seconds, but he computes that A's clock has advanced years. Now for B this may seem entirely as an abstraction, much like the Andromeda paradox: when you hang a U-turn on the autobahn, "now" on Andromeda can change years--but what does that mean to you: nothing.
Using curved space time do reduce g-forces during the run-to-bike transition has no effect on the paradox.