I've owned a D340 since last March and have went through the gauntlet on tuning and other little tweaks. Without a doubt, the best shooting and quietest bow I have ever owned.
In order to get the bow timed and sync'd correctly, you really should have a draw board. I put a new set of VaporTrail strings on mine and it took me an evening of tweaking to get it exact. Max the bow out and ensure it hits peak or advertised weight. If not, twist up both cables until it does. Keep an eye on your DL while doing so as you might have to put a few twists in the string as you're doing this. Once it hits peak, just make sure your BH and ATA are close to advertised. Remember, there is a +- variation on these measurements. As long as its within 1/8", you should be good to go. Then use the draw board to twist and twist each yoke to set pre lean in the cam, then use the control ends of the cables to get the timing/sync correct. Remember, timing on these bows MUST be set at FULL DRAW, meaning the stops hit at the same time. Don't pay too much attention to the timing dots other than to ensure you're inside of them.
As for the string stop. Mine made the hollow sounding noise too. Like stated by a few, just fill it up with silicon and your done. I have nothing on my string other than the speed nocks, peep and string loop and no silencers on the cables. This bow is frighteningly quiet, as I found out on the two deer I killed this past fall. I was actually astonished with how quiet it was out in the woods when I shot them.
The ONLY thing about my Destroyer I don't like is the grip. I got used to it, and I shoot it very, very well, but I prefer the feel and look of side plates and am going to swap out the grip for Torqueless plates soon.