Ground wire size for meter pedestal to subpanel
The grounding conductor is sized based on the largest ungrounded (hot) conductor. So if you have to use a larger ungrounded conductor due to distance, the grounding conductor will scale up as well.

8 AWG CU ground is good for up to 2 AWG CU ungrounded (hot) conductors (If I'm not mistaken).



250.122 is for sizing equipment grounding conductors. The ground wire running from the meter to the panel is not actually an equipment grounding conductor, it's actually serving as a grounding electrode conductor. Which means it should be sized based on 250.66.


    


You might want to ask your local building department, as they might allow you to use 8 AWG.  After all, I'm not a professional, so I could be interpreting the code incorrectly.