Low Noise Tube Suggestions

I recently swapped a solid state DAC (Muse 296) for a tubed unit (Lector Digi 2.24). I really like the sound now, but there is a little too much tube hiss. I find it distracting in between tracks or during very low passages. The Lector (and the Muse before) feed Audio Mirror SET tube amps directly (no additional preamp). With the Muse it was absolutely quiet, but with the Lector there is significant tube hiss. The gain of the Lector DAC is quite a bit higher than the Muse (3v vs. 1v).

Can anyone suggest some very low noise tubes to use in the Lector DAC? The previous owner provided two sets (CVC ECC81 and Fender 12AT7) but both sets are too hissy. I would also if possible prefer a set with somewhat lower gain. NOS tubes maybe?

Thanks in advance.