ime moderns are pretty high output. They tend to slam the front of amps, so I tend to roll off my volume to get decent cleans.What kind of amp are you playing on? I don't know what the Fishmans are capable of really outside of sound clips, but I remember seeing Mark Tremonti play through Fender Twins for his clean tone if that helps at all. Pretty much the bar for a great clean tube amp sound.
It could be that the Moderns are just a bit too hot or the EQ is too mid-forward. You could try backing down the pickup height some on the neck pickup and scooping some of the mids for the clean sound on the amp.