The sound you are getting now is 90% a result of your preamp. Even if you change the amplifier, you will still have the Moon 390 dictating much of the flavor of the sound.
Upgrading your preamp ( or adding one to the 390 DAC) is the key here. The Bryston 4b3 is more than qualified to amplify the signal he is receiving upstream. That amp will give you what it is getting from the preamp.
My suggestions of preamps for you to try:
McIntosh C2700, ARC Ref6 SE, Linn Select DSM Katalyst, etc.