[crackle]

The plastic shaft is very easy to cut to length and if the flat is filed carefully, with just a fine flat, the knob should push onto it and grip the small flat sufficiently. If not then make the flat bigger and pack out the flat with a thin piece of hard plastic and try again.
Alternatively, am I right in thinking the knobs are not the original ones, maybe keep the new shaft long and fit a new knob with a grub screw to the new pot shaft.

But you may be able to clean up and get the existing pot working nicely.

One point I have noticed about a radio with a non working oscillator, you can sometimes use another radio to get the faulty radio to work.
By tuning through the dial on the good working radio you may hear stations being received on the faulty radio.
It is rather spooky when you adjust one radio and the other starts to receive a station.

This can be even more noticeable if you are using an RF frequency generator. As you sweep the frequency generator across the MW frequencies + the IF frequency the radio should start to work.

Mike