Hello Trapper04. I have to say I'm surprised to hear anyone would consider carrying a Browning BPCR on a "backpack" hunt. These rifles are quite heavy. The approximate unloaded rifle weight without the rear sight attached is listed as 11 pounds for the .45-70. Add the rear sight and the necessary rounds or ammo would make it quite a load for backpack hunting.
With the above in mind, to answer you other question, I know from well-placed sources at Browning the BPCR's were tested well in excess of any of the published smokeless "hot" .45-70 loads, including those for the Marlins and Rugers. I personally would not hesitate to shoot any reasonable smokeless load in the Browning.
But let me make it clear I have not shot smokeless in mine. I have several Browning BPCRs and have only used blackpowder so for. But I have done extensive research on the Browning BPCR and on several occassions discussed the design and testing of the rifles with it's designer at Browning and all of the supplier of components for the rifles, including Badger Barrel (the barrel supplier).