Try it with the AM-FM tuner or some other source that has a volume control, like your phone.Will a bad cartridge only allow sound from one channel? I have good sound on one channel, but very muted on the other. If I hook up both green speaker wires on the loud terminal, all the speakers sound good. But I think I only have one channel working.
Without a digital voltmeter, isolation transformer and a healthy respect for the high voltages inside of that little amp I think you are confined to parts swapping ie: try a new 6eu7.I cleaned the pins and reinstall it several times. Still no change. Not sure what only half a side working looks like.

Doesn't one heater circuit heat both halves? Just pulled one out of my 9300.Can't really tell if both halves of the 6EU7 is working. Look at the bottom. It has two identical triodes (plates) inside and both have heaters (parts that glow in the center).
Turn it off and pull the 6EU7 tube and take a look at it and you will see what I mean by both (2) halves. Essentially it has two identical tubes inside one bottle.