Since all the voltages read somewhat low, I replaced the 3-element can capacitor that filters the power supply. AM broadcasts came in loud and clear. Since it was late at that point, I called it a night and put my tools away. When I turned on the set the next day, it was back to square one. The set's audio stage seems to work fine, but no RF signal is getting to the audio stage.
Nothing is heard in the phones or speaker, except background hiss from the audio.
Next, I replaced most of the remaining electrolytic and tubular capacitors in the set, just on general principles. This resulted in very clean-sounding background hiss, but still no signal. Checking the tube voltages against the values given in the service manual, I found a number of values that were out of spec, but no smoking gun. After that, things got really busy around here, so I finally threw in the towel and took it to a local shop for repair. Now the radio works and sounds great.