A lot of people over the years have reported rather poor accuracy using .30-06 in Winchester 95s chambered in .30-03.
As far as I know, .30-03 brass isn't available, and hasn't been for a long time.
But there is an easy solution...
Necking up .270 Winchester brass.
The .270 Winchester case is the exact same length as the .30-03 cartridge, and in fact it appears that the .30-03 was the base case used in developing the .270.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.