That little rubber insert isn't going to make enough noticable difference, but if you think you want one just call customer service and they'll probably send you one.
As far as rests go if you want "quiet" then you need to get a rest without moving parts. Of course that means probably "NOT" a drop away. I guess it depends on what you are using the bow for, but I've tried a ton of droppers and still have one on one of my bows, but I don't use one on a hunting setup.
For a 3D or target setup I don't think you can beat a blade or lizard tinguw style rest. There's just nothing that can go wrong with them. That may be why they are the overwhelming choice among more knowledgeable, less faddish shooters. Those who prefer simplicity and total reliability.
I don't think there is any type of rest that is a perfect choice for everything, but I like a blade for 3D/target and something like a prong or even a Star Hunter on a hunting bow. Heck, even a Whisker Bisquit for hunting if you have good follow through. I don't shoot high profile vanes like Blazers and have never had an issue with fletching clearance. I have never shot a bow standing on my head so this fad about arrow containment has never sparked any interest for me.
If You're Not Living on the Edge You're Taking Up Too Much Space
Martin/Rytera Staff Shooter
PSAA Life member, UBP Life member
PADI AOW Diver