Will the reason behind this so called drive-line slop, is a combination of several factors. You are sitting very close to the drive train, the trans, diff, and u-joints in this car are huge compared to your typical family car, and this enhances the feal and noise. If the car did not have the center console on it, you would just about be able to touch and see every component in the drive line from the front of the transmission to the differential yoke. Most cars on the market also have dampening feutures in the clutch. Many cars have now have rubber flex joints instead of steel u-joints, not to mention fluid filled hydro motor mounts. All these things are not desirable in a true sport car. As you become more accustomed to the car, this will lessen.
One thing you can't do in a parking lot, is give partial throttle when loffing around looking for a place to park. You must accelerate and fall back to a idle. The car will back lash if you don't do this. This is partly due to the engine computer, as it can not smoothly control the engine speed at fast idle.
You will get very used to this after in a few months of driving.
ps, as for the Z06 not having or having these issues. There engine is much smaller than the Viper. They run the same T.56 trans, but a lighter version of it. They may have a better idle motor setup and this may help in that area. GM cars really are advanced in electronics and daily driver comforts, without sacrificing much. I give them credit for that.
