Forgive me for questioning you, but something does not seem right. Have you
checked the good S-20R to make sure that its oscillator is 455 kHz above the
received frequency and not below?

I assume the trimmers are mica. You can roughly check the capacitance by how
tight the plates are meshed. Are the capacitors in both radios about the
same?

I still think you are aligned to the image and the method you are using is
confusing you.

Try this. Take your good S-20R and set if for say 10 MHz (wwv is good).
Then, listen to the oscillator. Assume that is 10.455 MHz. Now, take your
bad S-20R and set the dial to 10 MHz. Then, set your Icom to 10.455 and
adjust the capacitor until you hear the oscillator on your Icom. It should
be working.

Get a cheap grid dip meter - they are quite handy, even though you have
figured out a good workaround.

Colin K7FM