If your float is 'zinging' under anytime you touch bottom you are A) either running way to long, or You have way to much weight and it's not setup correctly.
On certain rivers you can run shot close to your bait and not hang up (Lake Erie south shore tribs for example) where the bottoms are fairly clear and not to snaggy. Do that on the Notty and you'll have a very crappy day. Different rivers call for different setups (obviously), but if you think I'm running 1-2ft above bottom and not just tumbling along like you are, you'd be wrong.