The typical .375 and .30/06 produce the same breech pressure, but with the larger case head, the .375 will put more 'strain' on the action.

Rod - the wood is a good note on your part - the 3rd shot with the 6 dram load split the stock of my double, but a proper repair and bedding fixed it permanently. The presures were low, but the recoil wasn't. Duplication loads with smokeless very much reduced the recoil - probably in 1/2.