Before starting any troubleshooting process with tubed gear, it's always a good idea to substitute new tubes first (or a stash that you know works). It's an expensive undertaking but unfortunately even new tubes can be defective or out of spec right out of the box. The Russian factories have a very low QC baseline which is why certain retailers (Upscale, TubeDepot, Viva, etc) are worth the extra upcharge for their burn and matching efforts.
Also, EL84's in push-pull pentode mode have very high distortion, up to 10%, once you get above a certain power, usually 10 or 12 watts or so, since all is needed is about a 5 volt swing to produce full power. The 12AX7 have a high amplification factor which can easily swing twice that voltage. So it is possible that you are maxing out at that volume pot setting.