Fred,
You are an engineer. That should be a very simple calculation.
The fact that you ran a large conductor to the grounding electrodes will have very very little influence on the resistance of that grounding electrode system.
The grounding electrode conductor is in series with the grounding electrode system. The resistance of #6 is 1.61 ohms per 1000' and 3/0 is 0.253 ohms per 1000'. If the GEC is 25' long and the ground resistance of the rod is 25 ohms, you would have a resistance of 25.04 ohms for the rod connected with a #6 and 25.006 ohms for the rod connected with the 3/0. How can this make any real difference in the performance of the grounding electrode system?
It was a rhetorical question; the 3/0 is indeed about twice the cross sectional area of two #6 (assuming for a moment it is even permissable to parallel ground conductors smaller than #1/0 - 310.4 - which could turn into a whole other argument).
I appreciate your resistance calculation, but again I'm hanging my hat on the conductor sizes presented in the table, as a fraction of the cross sectional area the service entrance conductor. It is my prerogative to err on the side of the
ampacity of the conductors connecting the service to the grounding electrode system - moreso than the resistance. I become more concerned with resistance at the grounding electrode system itself. I've spent many Saturday afternoons at commisionings watching electricians drive 20-30-40' of ground rods to get a meter to read 25 ohms; that meter was never connected to the grounding electrode conductor.
We engineers "hang our hat" a lot on tables like this, especially when they have been codified by federal, state, and local governments, and in court you could imagine how convulted it could be to convince a jury of this sort of technicality. I understand these system come across as "unecessary" or some sort of "black art" to many - although rightly or wrongly the local utility company in my region has been held liable for damage to equipment in residences due to improperly installed grounding systems, and for that reason, they require at least two ground rods and and inspection prior to turning on service. The moment I sign a drawings, I inherit the same potential liability, so I will err on the side of using the tables.