I've wondered not about hunting, but loading up a 7.62x39 version of the 300 AAC blackout.
Use a large 308 bullet, and keep it just under the speed of sound. With a expanding design, it would be quiet, and quite effective on deer too. (Something along the size of 300gr. with a ballistic tip?)
All I've used is Herter's SP and HP ammo, as well as Wolf HP and of course lots of ball and some AP loads from Egypt that were so hot, they really tear up the range stands. (IE cut metal in half when you really did not mean to.) The Egypt stuff had really hard primers that the Mini 30 did not always like on the first try too. (Firing pin does not protrude enough stock, as Ruger is worried a longer pin will puncture domestic loaded ammo.)