Have you checked to see that L3 and L15 show a proper peak when adusted? L12 is in the AM-only signal path, but the peak on that one tends to be so broad that it's hard to discern.
There are a handful of parts used for AM receive only that won't affect sideband. I have seen X1, the 7.345 MHz crystal become weak and cause this. Not a common fault, but easy to check if you have a spare crystal. Simply touching the two leads to the solder pads under the factory crystal will bring up the AM receive level if the old crystal is bad. No need to unsolder it to try this.
If C62, a 1uf electrolytic cap goes bad it can affect the AM more than the sideband. Likewise, touching the two leads of a new part to the solder pads under C62 will bring up the signal level if this is the cause.
The 455 kHz AM-only ceramic filter can go bad, but not all that often. Tapping it with a fingertip can reveal a mechanical failure inside that part.
Those items are the "hit parade" for this fault in my experience.
73