Third solution is that you re-place the ECC99 with lower gain tube with good linearity, similar plate resistance and operative anode current so that it will match the transformer in the same fashion. This could be the type 76, or the more compact 6P5GT, for example. But you will need 2 of these and so it would not be straightforward replacement.....
If you instead want to use the 6SN7 you could configure it like a cathode follower but you will need to put an input capacitor to remove the 39K from the plate and place it in series with the cathode resistor you already have. The grid resistor would be connected anyway between the cathode resistor and the 39K resistor for the correct bias. The cathode capacitor will be removed. The output of the cathode follower is taken from the cathode....
Respect to the ECC99 alone this solution would present easier load to the source as the input capacitance would be much lower.
Also if you decide to go for the ECC99 only you will need to check the voltage supply as it will draw less current and other voltage supplies in the circuit might increase if not regulated.
Thanks! I guess if the two ways that I stated don't work too well, I will just go for ECC99 only (actually I have changed it to Bendix 6900, which is a little bit lower gain compared to ecc99). And you are right about the voltage supply, which is what I am little bit worried about. Not sure if I can handle it correctly without burn the pre down... Cathode follower would be a bit too bold at the moment I guess.