I think you are over analyzing the whole thing.
The strings he used, as well as the tone, the string mute, etc., were pretty much the standard electric bass tone at the time. If you went to a store and bought a brand new bass, it had flats, and a string mute as standard.
I didn't know who jamerson was when I was starting, but I grew up hearing Motown, and the Beatles. I bought LaBella flats for my Teisco bass. That's what they sold at the local record store, and that's often where you bought stuff like picks and strings. I got some foam rubber and stuck it under my strings. I used that same tone, and everyone I heard used that tone. That's what electric bass sounded like, until a little later with Jack Bruce and John Entwistle and others.
Even my brand new Ric 4001, which I bought in 1973, had flats and a string mute. I don't remember if the mute was engaged, but on Fenders you had no choice, until you removed the bridge cover. I played with those flats for a year or so and then got my first set of Rotosounds.

I don't recall seeing any basses sold new with roundwounds until the 80's.
And some people added another piece of foam to make the strings even deader. I had a Paul McCartney songbook that showed him with a big chunk of foam under the strings by the bridge. Carol Kaye made that sound famous as well.
As far as Jamerson playing with one finger... he was an upright player, and that's pretty much the normal way to play. You also get a more consistent tone from note to note. His particular hand position was very unique to him though, and once again is him coming from an upright and finding what he was comfortable with on electric.
We don't know for sure that the board used tubes, but surly a lot of the gear did. But his direct signal doesn't sound particularly tuby. Mike Mclean built the console and much of the studio. The "farty" tones on the bottom string was common for a P played with force. It's also good recording practice to keep your levels hot onto tape.
I think they just went for good tones, and they also used a lot of compression wasn't as common at the time.
Here's the console
http://www.flickr.com/photos/7576734@N02/846246970/
Just to put it into perspective, here's Paul McCartney's bass from a Day in the Life.
So what do you notice? It's a very similar tone to Jamerson's, even down to the farty low notes, even though Paul is playing a Ric bass with a pick. I'd imagine it's the stock Ric flats (made by Maxima) and he sounds like he has extra foam under the strings near the bridge. DI recording, into...? Who knows. I'm not sure what consoles they had at Abby Road, but I'm sure it's not hard to find out.
Link Removed
So it's not all that far from the Motown sound, which Paul emulated, but his playing is different. And Ringo is a very underrated drummer!
(as a disclaimer, I posted this purely for educational purposes)