Tubes can also cause popping but since it moves to the other channel with a cable swap seems unlikely.
The tubes in that preamp are all twin triodes (12AX7’s and 12AT7’s), so it’s possible that one of the two sections in a tube (serving one channel) is bad but the other section (serving the other channel) is not.
The only remedy I have found is to engage the phase inverse on the pre. The hum is greatly reduced, and both speakers play at equal volume. Also if I engage the mute button on the preamp, I do not get a pop in the speaker when I power on the power amp.
When you toggle the polarity ("phase") reversal do you hear a relay clicking, and when you engage the mute function do you also hear a relay clicking? And if the answer to both questions is "yes," do the clicks in the two cases sound similar, and like they are coming from around the same place in the unit?
What may be an interesting clue is that the input impedance of your power amp is vastly lower for its balanced inputs than for its unbalanced inputs. The specs are 2K and 50K respectively, and Stereophile measured 926 ohms and 49.2K respectively.
What I’m thinking is that the RCA output of the preamp may be driven by one of the two signals that is provided to the XLR output (which is done in many designs), and the output coupling capacitor through which that signal is processed may be defective. And if the answer to my questions about the relay clicks is "yes," when you reverse the output polarity you are probably changing which of the two signals that are provided to the XLR connector (one being defective and one being ok) is provided to the RCA connector.
And when you use XLR interconnections the very low input impedance of the amp essentially shorts out whatever combination of leakage and/or distorted signal is being provided by the defective capacitor, resulting in the amp simply responding to the good signal in the balanced signal pair.
Although as I said earlier, it is also possible that a bad tube is responsible.
Good luck. Regards,
Edit: Although if my hypothesis is correct I would expect that the two speakers would not "play at equal volume" when XLR interconnects are used. I would expect there to be a 6 db volume difference. So I’m not sure how to explain the equal volumes you are hearing when XLRs are used. But I still suspect that the amp's vastly lower balanced input impedance, compared to its unbalanced input impedance, is somehow involved.