Success!
I removed the stock to better get at the innards. Everything looked good inside, perhaps a little bit of dirt and crud, but nothing surprising. The wrist of the stock does show some staining from decades of oil and being stood muzzle up, this is not surprising for a field grade gun that probably got plenty of use in the last 92 years. By the way the gun has Chicopee Falls barrels and the barrel flats do have the correct serial number that matches the receiver and trigger guard. I'm guessing that this was either a gun that was serviced by Savage and the old barrels replaced, or the gun was a parts bin gun built later, I have no way of knowing.
Upon close inspection of the trip there was only a very slight buildup of oil. It came off with a gentle application of 91% Isopropyl Alcohol using a Q-Tip. A pipe cleaner with the same alcohol cleaned out the channel that the trip moves in. After cleaning I allowed the alcohol to evaporate and then lightly lubricated everything with Hoppes #9 Lubricating Oil and wiped off the excess. I reassembled everything and... FAILURE
The problem was only slightly better and the lever returned to center about half of the time.
After several minutes of angry frustration and reflection I closely looked at the top of the trip with the barrels removed but the receiver and stock otherwise fully assembled. I noticed that the trip was being held in place by the pressure of the internal spring, but that pressure was not particularly forceful. I was able to move the trip sideways easily with a small screwdriver. Hmmm, perhaps more spring tension would solve my problem? I removed the large trigger plate screw and extracted the spring and trip. I counted the coils and the spring did not appear to be broken or missing any coils when compared with photographs of the spring that I found on the internet. OK, so far so good. I then took a couple of knife blades and grabbed the spring at the final coils on each end and gave a gentle stretch. I did not add much length, perhaps only equal to what one or two more coils would have been. I reassembled everything and viola! SUCCESS! The trip was now held in place securely by that now slightly longer spring. The trip moves freely in the channel but is not easy to move with a screwdriver as it was before stretching the spring.
I will order a replacement spring and keep an eye on the original. If the problem returns I will simply insert that replacement spring.
Let's face it, as we all know a gun like this is nearly a century old, springs will loose some tension over the years. I do not find this particularly surprising. That is the joy of using a fine old gun like this.
