Dmitrydr, like the other poster here, I think a cable swap may be a good place to begin.
I'm using Acoustic Zen Silver Reference II, Matrix II and Hologram II in my system and enjoy the sound very much. The Silver Ref II and Matrix Ref II do sound very different, the Silver Ref II is leaner and more detailed because of its silver composition and the Matriz Ref II is fuller and rounder because of its copper design. But they share a signature AZ smoothness, and work well together in the same chain.
I used to own the Simaudio Moon I-5 as well, and am quite familiar with its sometimes thin, bright nature. Cardas Golden Cross helped to tame it to an extent, but I realize your problem is the opposite of what I experienced with the I-5 three years ago.
A recent thread commented on the differences between Cardas Golden Cross and Acoustic Zen Matrix Ref II interconnects. I never did a direct comparison, but the other posters did. They remarked that the Matrix shared the same smoothness and warmth of the Cardas, but with better extension on the top end along with a bigger soundstage.
While the Silver Ref II is by no means a bright cable, it is silver and will therefore be leaner than the Matrix Ref II. I think the Matrix Ref II may help you and will definitely be a big step above the Monster cable you're using. It's also half the cost of the Silver Ref II.
You should be able to snag a used Matrix Ref II for about $350.