It seems like a no brainer. Your tubes are used up and/or have always been noisy. This unit requires low noise AND rugged tubes. It has a reputation for that which precedes your problem.
FWIW, in light of other advise to the contrary, the line stage follows the gain controls. The volume controls only attenuates the volume from the sources before it gets to the line stage. Any noise from tubes or anything residing in the sources, including phono, would be changed by rotating the volume controls, but noisy tubes in the pre-amps line stage would always be constant. The extent that noise from the line stage would be heard would depend on the efficiency of your speakers, input sensitivity of the amp, and of course the quality of the tubes.
Most owners of this unit end up using something like NOS 6h23EH which are both rugged and (usually) very quiet. FWIW I have identical issues with my ARC SP10 and ended up using 6h23eh in the line stage tubes. Unless you get the right tubes in the first place you can easily burn them up in 100 (or less!) hours, and you can easily burn up a lot of dough trying find tubes that will perform right in this pre-amp.
This is any old and often discussed issue with the AI. Do some research in the forums and you'll find them.
Hope that helps a bit.