An update to my post#20..
With a some more searching, I found that the Fed Gov't under the Fed Firearms Act 1938, ammended that law in July 1958,
Required all centerfire long guns and all Handguns regardless of caliber mfg'rd in the USA to be ser#'d.
Cal .22rf long guns and any shotgun were excluded from the ser# demand though mfg'rs could (and did) ser# them if they wanted to do so.
(The GCA68 removed the exclusion from ser#'s for the .22rf Longguns and all shotguns. That made 'all firearms mfg'd in the USA required to be ser#'d'..
...Though 2 classes of the 4 already had been so since July of 1958)
So,,I can only assume that the Savage 340 (and Model 219) ,,possibly others? that are about that are unser#'d are pre July 1958 production.
That the IRS/Treasury did come down on Marlin for their unser#'d 5000+ C/Fire Levermatics was because it was in 1963.
https://archives.federalregister.gov/issue_slice/1958/1/18/339-347.pdf#page=5
Regulations implementing the Federal Firearms Act of 1938 required all firearms manufactured after July 1, 1958, to be identified with the name of the manufacturer or importer, a serial number, caliber, and model.
Internal Revenue Service, Department of the Treasury, 23 FR 343 (Jan. 18, 1958). The only exception from marking the serial number and model requirements was for shotguns and .22 caliber rifles not subject to the NFA.
As Listed in the Federal Register Jan/1958
SUBPART D— CONDUCT OF BUSINESS
§ 177.50 Identification of firearms.
Each licensed manufacturer and importer of a firearm produced on and
after July 1, 1958, shall identify it by
stamping (impressing), or otherwise conspicuously placing or causing to be
stamped (impressed) or placed thereon,
in a manner not susceptible of being
readily obliterated or altered, the name
of the manufacturer or importer, and the
serial number, caliber, and model of the
firearm. However, where imported firearms are identified by the foreign manufacturer in a manner prescribed in the
foregoing sentence, additional stamping
will not be required if the information
prescribed by this section appears. However, individual serial numbers and
model designation will not be required
on any shotgun or .22 caliber rifle unless
such shotgun or rifle also is subject to
the provisions of the National Firearms
Act.