So back to the issue. Since this radio has a three gang AM tuner
"front end" board, I should be able to prove or disprove your/my new
theory, by injecting an rf signal somewhere between the front end
and the AM/FM board. There is an interconnect schematic here

http://www.hifi-museum.com/lib/misc/...-sx-727_sm.pdf

on page 15. Where would you suggest I try and inject signal?????

I don't see the AM front end on the interconnect diagram -- only the FM
front end. The AWE-015 is designated the FM AM Unit.

If you look at the AWE-015 schematic (page 24), you'll see the AM input at
pin 18. Q11 is the RF amp (I assume), Q12 is the LO, Q13 the mixer. The IF
goes to Q4 and Q5, which feeds T5. And then the detector.

You need to signal-inject/signal-trace along this path. Did you say you had
a 'scope? A 'scope can be very useful, as even the cheapest of 'scopes can
display well past the AM band.