I apologize again for the delay. So I ran a few tests with the proper and improper threading technique and the shakes have reduced quite drastically! I may add to this as time goes on but for now, I think you pretty much fixed the problem, Rolf! Thanks a million, once more.
One might say that the previous owner's abuse of the machine is something of a blessing in disguise, seeing as how this may prep me for repairing my Tascam 38, if need be. It's kind of surprising just how easily maintainable these machines are and how you don't need a microscope and tweezers to get things going again.
Anyway, this machine has been owned by a smoker and perhaps that may explain the stains on the dress panel. But the other non-cosmetic flaw is that the inner and outer knobs (line, mic, and output as shown in your picture Rolf) can't move independently of one another unless I use both hands to either hold one or move both in opposite directions. I imagine the solution to this will be much easier than the oiling business. I'm kind of glad that my dinky 23w soldering pencil could adequately do the job. I was afraid that I'd have to replace it.
I may have to buy another take-up reel though because the tape still twists along the inner side of it, despite all attempts at adjusting the screw on the nabs that allow for moving the reel table heights.
songjohn- yeah, VintageTexas' video and pictures show how my machine could look like. The grain of the metal is just stunning!