Okay, I have the beast at home, it is thoroughly cleaned inside the cylinder and barrel, has been appropriately oiled, and checked for any mechanical difficulties. No pitting nor deformities in the barrel nor cylinder. There is holster wear along the sides of the barrel with some scratches.
The crane was difficult to get out due to sludgy oil buildup and incredible tightness--after cleaning and removing the old sludge, went back in without a problem. Took off grips, all appeared to be fine there and you can see why the Old New Service does not exhibit nearly as much stacking as the Police Positive or the Official Police. Due to the size of the revolver, the v main spring is nearly straight on in geometry versus the greater angle that the smaller revolvers require due to smaller size. There is just a hint of stacking versus the more substantial stacking of the small Police Positive with the OP falling between the two.
There are a couple of places of freckling that was taken care of and the backstrap and butt have little bluing left with a darkening of age and probably hand oil over the years.
I have taken a picture of the apparent TVA markings that appear to be crudely etched on the backstrap. The apparent rack number is also crudely scratched on the revolver butt which matches the backstrap number. The lack of bluing wear on the inside of the frame between the butt and trigger guard seems to indicate this weapon was mainly carried versus being shot. The bit of trigger guard wear is far forward that may indicate some sort of holster allowing access to the trigger in the holster which was common in those day. It is a 5 inch barrel model and the date of the mid thirties by Colt Serial Number indicates appropriate age for possible TVA use. It is known that the TVA bought .38 Special Colt New Service Revolvers in the 1930's with a 5 inch barrel.
From Paul Scarlatta's article in the Shooting Times on the New Service,
"The New Service in .38 Special was popular with police and was used by the Texas Dept. of Public Safety, U.S. Border Patrol, Pennsylvania State Police, Kansas Highway Patrol, the
Tennessee Valley Authority, and San Antonio and Richmond police departments. The New Hampshire State Police bought some in .357 Mag."
https://www.shootingtimes.com/editorial/handgun_reviews_st_coltnewservice_200905/100072
From Bob Murphy's booklet on the Colt New Service via Gunboards,
https://forums.gunboards.com/showthread.php?68061-Colt-New-Service-which-PDs-used-them
Murphy lists the TVA as purchasing .38 Specials with a five inch barrel (see Doughboy 1953 post midway in the forum postings)
https://forums.gunboards.com/showthread.php?68061-Colt-New-Service-which-PDs-used-them
Thus, the TVA bought and used .38 Special New Service Revolvers. Holster wear patterns and also little internal wear indicates a weapon that was carried more than shot. The markings themselves are crudely done which detracts from the TVA use possibility slightly. That mystery will have to wait until I can try getting a letter for it and I will update with a range report. I'll try 158gr. lead SWC's first and some 148 gr. wadcutters for accuracy testing.
Some additional pictures attached.