Problem 93. A couple of SG 3x3 magic squares composed only by distinct palprimes

Around January of the year 2001, my friend Jaime Ayala constructed the following pair of 3x3 magic squares, composed by 18 distinct integes palindromic & Sophie Germain-alike from one square to the other, but only a few (4) of them being primes. This was the starting point of my puzzle 124.

Here is the pair of SG alike 3x3 magic squares, gotten by Jaime Ayala

Palindromic but not all primes in a Sophie-Germain-alike pair of Magic Squares, by Jaime Ayala, January 2001
252	171	363	-->	505	343	727*
373*	262	151*	2.n+1	747	525	303
161	353*	272	-->	323	707	545

The 18 integers are palindromes but only 4 of these integers are primes*.

Very optimistic we posed the following only & apparently simple question:

Can you produce one of this type of pairs of Magic squares (SG alike) , but using exclusively (distinct) palindromic prime numbers?

...

The response of our readers was a noisy silence... Until just 25 years later, exactly the past May 15, 2026, Arina Bator one young Polish student of the Jagiellonian University in Cracovia, sent an almost solution to this old puzzle:

Almost Palprime &  SG Magic Squares by Arina Bator, May 2026
1925356557556535291	1529480708070849251	1727253646463527271
1529260726270629251	1727363637363637271	1925466548456645291
1727473628263747271	1925246566656425291	1529370717170739251
3850713115113070583	3058961416141698503	3454507292927054543
3058521452541258503	3454727274727274543	3850933096913290583
3454947256527494543	3850493133312850583	3058741434341478503
Qualification =13/18	72.22%
Fails = 5 integers
Integers that are Palindromes but not Primes
Integers are neither Primes nor Palindromes

We have learned that each puzzle finds out finally his appropriate puzzler. Arina Bator will be known as the first producer of a good near-miss solution of this puzzle.

Q. Can you produce a complete solution to this puzzle or at least a solution with greater Qualification than 72.22%?