I tried doing an alignment and discovered a broken slug in the IF can on the tuner. I suspect it broke when someone tried to adjust it because it's an odd design in that it performs two functions. The top slug is for video and the bottom for audio. You need to use a very slender alignment tool passed through a hole in the top slug to adjust the bottom.
It's L106 on the schematic. I think every other split carrier set I've encountered has the audio trap on the main chassis and the tuner has a single output. Admiral made this change in later models too.
Luckily, I had a spare tuner and popped it in and proceeded with the alignment. That solved my problem of lousy reception on channel 4, but the sound was still bad.
So I proceeded with the alignment and ran into another problem. Some of the IF coils don't peak. In fact adjusting the slugs seems to have no effect at all.
I decided to pop out the first audio IF can (T201) for a peek inside. Sure enough, it has the type of exposed mica cap that so often go bad in radios.
I carefully disconnected one end of the coil in parallel to the the cap. I measured no capacitance and it's very leaky on even the lowest voltage range!
Unfortunately, I don't have any 30pF micas on hand so I'll have to order some. Might as well get some for the other IF cans as well.