Is it possible to use two different metrics for one observer in distinct times (related to twin paradox)
I am not going to rewrite another twin paradox, what i am interested now is that if we assume an observer who moves with acceleration first (during $0<t<T_0$), then he stops his acceleration and moves with constant velocity (during $T_0<t<\infty$), is it possible to use two different metrics (one for his acceleration (like <PERSON>) and another for his constant speed) to see what he observes in the universe? My first guess was that it should be ok, but actually it's not. And if it's not really ok, how are we going to describe his frame?
My problem: Assume two observers S and S' who are at the rest in $t=t'=0$ but at different places (they can synchronise their clock by exchanging signals, because they are the rest). Now observer <PERSON>' accelerates with $g=210^8 m/s^2$ in its frame* for one second, just after that he stops this acceleration and moves with constant speed toward S. We want to show that S will be older than S' according to S' when they meet each other at S's place, by using S' proper time which we can derive from its metric. However though, if our observer accelerate for a mere second we can see that S will become older only for 1.07 second,
https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)
$t=csinh(gt'/c)/g=3sinh(2/3)/2=1.075s$
Where $t$ indicate S elapsed time. This is expected and fine because our accelerated observer sees a faster clock for S. But this is where we encouter a big problem. 272
If we assume that after acceleration (when S' becomes inertia) S' can use <PERSON> metric, then due to the gamma factor for the remaining path, he will see a slower clock for S, and if we make their distance large enough, we will see that according to S', S will be younger in their meeting. (gamma factor should be around 1.34, if S' arrive at S location 1y later in S frame, according to S', S' will be 1.34y old while S is 1y old, and let's forget about that mere 0.07 second!). This is twin paradox because S will consider S' younger too. where did i go wrong? Do note that i just said this problem as an example, my question is in the title so don't try to solve paradox without answering the real question.
P.S: I saw around 6 pages of physics.stackexchange about twin paradox. Didn't find something like my question, in all of them S' was considered to be accelerated all of the time (when they wanted to calculate elapsed time directly in frame S') which solves the paradox clearly. However if my question is duplicated, please do enlighten me
Update: Note that we are going to write worldlines in a coordinate system that S' is always at the rest at the origin of coordinate system. We have no problem in the S coordinate system as it was done by @ChiralAnomaly 272