Your release, nock fit, and tuning are my first thoughts.
How the string is made and the string material itself are second.
I've run across a rare bow that seemed to "like" one material over another. Couldn't say why, it just shot quieter.
On the several bows I've tried it on, I haven't found "skinny" to be any quieter than a moderate size string (both equally well made). I did have one bow that was noisy with a way overbuilt string.
Don't forget silencers can be tuned. I've seen a few bows where moving the silencers made a HUGE difference in noise.
First thoughts are it's a vibration problem, because with the quiver it's quieter--the quiver acts as a dampener. That's likely tuning...maybe the nock set needs moved up or down, and/or your release may be part of it.
Last resort for me would be a different string. I've had fantastic results with 18-20 strands of BCY-X.
Chad