One thing no one has asked about so far is whether you have tried both of the output taps on the amp, and also whether you have tried the amp in both ultralinear and triode modes.
If you are presently using the 8 ohm taps, and haven't tried the 4 ohm taps, you should definitely do so. The impedance curve of your speakers, as shown in Figure 1
here, suggests that a fuller sound is likely to be realized with the 4 ohm taps (although using the 4 ohm taps with the X12 may reduce the amp's maximum power capability slightly, compared to the 8 ohm taps).
That is particularly true because the Dialogue Five is described as using zero feedback, which is suggestive of a relatively high output impedance, which will be highest on the 8 ohm taps and will interact significantly with the wide swing in speaker impedance that occurs between around 200 Hz and 1.5 kHz.
Whether you use UL or triode mode is also likely to make a significant difference. As would changing power tubes among the numerous kinds the amp can accept (EL-34, 6550, KT88, KT90, 6L6GC, KT66, 7581, EL37, etc.). As would changing the small signal tubes in both the amp and the preamp. I (and others here) have found with other power amps that the choice of small signal tubes can often make more of a difference than the choice of power tubes, and can often mean the difference between sound that is unacceptably thin, and rich, satisfying sound.
Good luck. Regards,
-- Al