[morzh]

Since the hum disappears in full when the 7AF7 tube is removed (it is the phono pre-amp) I knew the tube somehow makes the noise.
Eventually, after tracing the filament supply (it is routed away from the input and as a tight line, plus it is a separate winding from the transformer with a centertap) and not being able to do anything, I decide to try to shunt the Cathode with a cap to the GND.

On one hand, that should increase the gain in highs (and i already have little base, only when playing the records, likely due to the amp being made for EM cartridge with transformer vs the piezo, which is what I have now), and this is not my goal.
On the other hand I could deal with this later.

So, I unplugged the phonograph, put the volume to the max, heard the hum, touched a 20uF cap between the Cathode and the GND and....the hum disappeared. Varying the values, I found that the same effect is made when the cap is 1uF, but the hum persists if it is 0.047uF. So I soldered a small 4.7uF aluminum can, plus to the K and minus to the chassis, and the hum now is very low, I have to really put my ear against the speaker at max volume to hear something which is more like some white noise rather than hum.

Playing the record (I use Luis Armstrong) revealed practically the same playback quality with a bit more volume and just a bit more treble (not really much more). Still the lack of base.

Since the base is good when the radio is in receiving mode, I think it might be the input filter that is sized up for ElectroMagnetic pickup and the transformer rather than a piezo crystal. Now I need to research the input filter parameters and try to make it play a better base.

Then hopefully I will be done.