The chance of the #6 bonding conductor becoming energized is much lower than that of the isolated ground rod and any parts connected to it. (Provided the connections to the existing electrical service ground are made securely, using connectors that are appropriate and the cables are prepped to remove corrosion and other sources of resistance.)
The goal is to minimize resistance/impedance between the two points being 'bonded'. If you use soil instead of copper, the resistance will be much higher, and quite variable. If you use wire that is too small, it may fail while conducting fault current. If you allow corrosion to remain in a connection, or use a connector that corrodes, you can expect the 'bonding' connection to fail... allowing a voltage difference to exist between parts that should be at the same voltage level.
I would verify that the heavy cable shown in the photo under your deck is the grounding conductor of your electrical service. If so, I believe that a split bolt connector such as this,
http://www.homedepot.com/p/Blackburn...B1-5/100125660 would be a secure means to join new #6 AWG to the existing. I would not rely on twisting or wrapping.
If the underside of the deck is inaccessible, there are connectors that can securely connect to the meter-base... which is also a legitimate point of electrical service ground. I would consult with an electrician if that was the route you needed to go.