Leaving aside issues with safety in reactivating a rifle that's been welded up, you simply do what Ordnance did.... bead blast it and parkerize it.
Bead blasting (NOT "sand blasting") doesn't damage stamps as badly as buffing or sanding metal does.
I've see some of the Korean surplus M1 rifles and Carbines which had been refinished so many times by the Koreans the lettering on the receivers was nearing illegibility.
How many times a rifle would need to be bead blasted to do that would probably be a good many.
Use a bead blasting media that isn't too aggressive and experiment with air pressure to give a good "orange peel" surface that doesn't attack the metal too much.
Most USGI parkerize jobs are actually rather smooth, not nearly as rough as say, a Remington Police shotgun is.