Lube
bearing shaft-----gently pull the drum out of the shaft, then you can wipe clean the spindle on the back. Then wipe on a few drops of oil. Also use a rag and a finger to gently wipe old thickened oil/dirt from inside the bearing inner tube/hole. The tube has a felt wick, use 3-in-1 or any thin turbine oil. Be slow and careful putting the drum back in or you'll squish that wick down the tube and have to re-assemble. Mine took two tries then fit together perfectly.Get real close up with your eyeballs and you'll see what I mean and how it functions and re-assembles. I think I also remember a small 2x4 wood block helping to hold the wieght of the drum up until I could get the front and cabinet back on to hold it.
The idler pulley is seated on a moving small backplate, the backplate needs a bit of grease, white lithium grease works well, on all the area that slides metal to metal. And the 2 ends of the idle pulley spring can use a small amount of grease where metal rubs metal.
I wish I had taken more pics of my 1960 to help, but if you take pics and post them as you dissasemble, we can advise from your pics.
And the motor likely needs a thorough de-linting. Hold it upside down as you brush it clean so dust falls out, not down in. Do this at both ends. Then more turbine oil down the shaft, into the bearings at each end. Go sparingly for 2 reasons: Not much gets in, and leftover oil attracts more lint.
We'd love to see pictures, and this cleanout/lube job will help your dryer run longer and a bit more efficiently, but not much quieter. As long as there's no squeaks or clunks, just steady airflow whirls and machine motor and belt humming routinely, it's as quiet as these designs ever can be.
I wish I had saved all my pics from my 1960 Kenmore tune-up, but I believe my memory is correct!