I only have a vague idea what Solo's and Autotest are, HRCR is told by google to me as historic racing and due to lack of knowledge and language barrier I don't know what atm, 12 cars and 2020s are...
Is this racing full on tarmac? As I have no experience on gravel... and only with brisk (polite aggressive) road driving. And our streets seams to be not as rough as British... yet...
But for the issue of the too soft sidewall I can share my experience.
My Mini started it's life with me on 12 inch Yokohama A539. It was converted quite a time ago to 10 inch and first I had Yoko A008 and took detours over Falken and Nankang (both not worth it) back to the A008 for a long time.
End of winter last year I finally dared to try the Yokohama A032r and regretted impartiality, not to have tried them earlier. They have so much more grip, surprisingly especially in the wet.
And for the question of the sidewall, the 12 inch A539 feels as soft as the 10 inch A008 but as the sidewall of the 12 inch is narrow, I assume there is now gain for switching to 12 inch.
But the 10 inch A032r as "racing tires" has significantly stiffer sidewall.
Oh, and of cause they make more noise...
So with the better dry grip, the much more better wet grip (even over the A539) and the stiffer sidewall if available I would recommend to give the A032r in the soft compound a try.
Please be aware, it's only my experience and only last year, where I sadly coundn't drive as much as I wanted, so it's limited to 3 oil changes or 9.000 mls...
Also I don't really have comparisons to any 13 inch tires as the Nankang NS-2R I drove briefly were in dry summer over only few days and fuel tanks...