My preference, backed by some experience, is to use a somewhat softer bullet for hunting that I use for target shooting.
With cast SWC 44 calibre hunting bullets alloyed to produce a hardness of about 15 Bhn, I have recovered some bullets in deer that expanded to ~0.65/0.70". Sure, the bore will eventually lead foul with bullets of this hardness if you're loading your 44 Mag to near maximum pressure, but if your revolver has a decent bore it will take perhaps 30 shots before practical offhand accuracy is much affected, more shots (I sincerely hope) than anyone would use in a day of hunting.
Bob