My thoughts (based upon experience with at least more than 10 BRNO´s M21/21) :

The barrels and stocks of those rifles are very slim , what makes them so attractive.

Reboring the barrel from 8mm to 9,3 results in very thin ( and light for caliber ) walls of the barrel.
Barrel mouth is very thin (too thin?) because the front sight ramp is sleeved .

Most of the very slim stocks were cracked inside under reccoil even in the standard calibers (8x60,8x57,7x64).The 9,3 will strain the stock much more.

The recoil of the 9,3x62 in the resulting very light rifle is not just that what I would name comfortable.

So I first would leave all the secondary thoughts about BM, bolt handle and so on and go for a new barrel with more flesh ( if it must be a 9,3x62).
Alternatively (copying the contour) chosing a cartridge in the .270 to 8 mm class.

Just my 2 ct.