If you want 357 Max power, you can get the rifle converted to the 357/44 Bain&Davis.
I once built an M1 carbine in 357 Auto Mag. You could probably modify the M1 carbine magazine to fit the magwell on the 77/357. 7 357 Auto Mag rounds will fit in the 15 round magazine and 14 in the 30 round M1 carbine mag. My M1 functioned perfectly but I had to drop the 357 Auto Mag loads by 10%. Still managed 2000 fps with a 158 gr JSP.