Before I respond to your post assuming it is a tube issue could you clarify for me what you are hearing.
As described I interpret your posts to say that when your original tubes (the 6H23's) are in the phono stage you are getting a hiss in the left channel. This is a problem typically associated with tube noise level (quality).
But you then say that when you change the tubes in the phono stage from the left channel to the right channel the hiss does not go away. That might mean that you have an electrical problem in the left channel alone! Otherwise if the tubes in the right channel were quiet in the right channel and became noisy in the left channel and conversely the tubes in the left channel were noisy in the left channel but became quiet in the right channel then I can only conclude it is not the tubes. This is furthered by the fact that when you put these same tubes in the line stage both channels became noisy!
I think you need to have your pre-amp visited by a technician.
FWIW, re tubes, new production EH6922's/6H23's (same tube I believe despite designation) and the NOS 6h23's, there is a substantial difference in tone if nothing else. If clarity is important to you, as it is me, I think the 6h23's are much better and very similar to NOS Sovtec 6922's if not identical if the noise level is the same. The EH tube is muddy in comparison. However if you think your pre-amp is already inherently bright and needs to be toned down, the EH's would probably do the job and I believe both are rugged enough for your pre-amp.
Hope that helps a bit.