[morzh]

Today spent some time trying to chase that hum.

One of the suspects was the capacitor: the cap in he radio that filters the plate voltage on the 6AF7 (the phono amp) is 0.1uF but the parts list shows it as 1uF.
So I put 1uF in parallel, no effect at all.

As I said, shorting the input of this tube does not get rid of it but shorting the output (or extracting the tube) does.
Also the hum is only exists with phono, not with radio.
So, after replacing the tube with the old one (weaker but works fine) with no results, I decided to leave the radio the way it is.
The phonograph with the new needle plays OK. There is a lack of base. I suspect the correction filter is there for the transformer and not the piezo. The radio itself has excellent base.

If I ever get the original phonograph cheaply I might put it back as the transformer is good, I checked it. But then it will not play 33-1/3 rpm records. Or I might get a phono preamp that matches piezo with EM input.
Or I even might sell that radio as I already have an FM with a phonograph.

There is only so much could be done with this without modifying the sch which I am not eager to do, I try to keep things as original as possible.

Now to putting Humpty Dumpty back together again.