Finish eliminating the easy / inexpensive possibilities, ie. the coax and matching transformer.
Next eliminate interference from equipment in your home (test by disconnecting the power to electronic equipment). Grounding the coax shield is a good idea, but it won't stop the antenna from receiving interference. The most effective way to deal with interference is to stop it from being generated. If you cant do that, then you'll need to find a way to put distance between the antenna and the interference generating device.
Still not fixed? Trees can be quite troublesome. Can you relocate the antenna to avoid the trees? If not, can you consider increasing the mounting elevation? A pushup type mast may help. Example:
http://www.3starinc.com/telescopic_masts_and_more.html When you click on the call sign of stations listed on your TV Fool report, you are shown a 'path profile'. In Florida it's rare to see much blocking terrain show up. In such circumstances, additional mounting height often produces more improvement in signal quality than switching to a larger antenna. (Though there are exceptions.)
Finally, if you have no alternative, then I'd consider going to a larger antenna such as the Winegard HD7698P.