No selectivity/Sounds like crap

[mr_fixer]

After re-reading the above posts i thought about something that may be affecting your am reception. I believe you said that this radio has a loop antenna? might try moving the radio around to see if there are other stations that are nulled out by being on the wrong side of the loop.
As far as those 2 bypass caps , try clipping one side where it would be easy to re-solder them, if it starts to oscillate. Try 1 cap at a time. Start with c29 that is the one i think does the most high freq roll off. It was put there for a reason, it might saved some cost than putting a better transformer or speaker in the audio section. Only your ears can tell.
Logan