The problem remains in the right channel after swapping output tubes left-right, trying another set of output tubes, and after swapping the outer pair on the VTA driver board left-right. I also swapped the speakers, and the noise could be heard only in whichever speaker is connected to the right channel.
Are the relevant sections in the troubleshooting sticky the following?
6. Problem - Hiss, noise, crackling sounds on idle
Areas to check - Noisy driver tubes, noisy resistor on driver board (especially older carbon composition resistors), bad solder joint or bad solder trace on the driver board.
7. Problem - Popping or snapping sound
Areas to check - Usually means that high voltage is jumping to chassis ground somewhere. Could be anywhere even might be inside a tube
I also found this suggestion for the ST-35: "Try powering up with the pre amp tube(s) removed for that channel, leaving only the EL84's in to see if the noise stops." (see Re: rushing with crackle sound coming from my ST-35. Which, I'm guessing, helps to determine if the problem is in the front end of the amp. Is this applicable as a trouble-shooting step for the VTA ST-70?
What else should I be checking: solder joints on the the right output tubes, connections between the right output tubes and the driver board, ...?