Despite the suggestion made by the nice drawing, I would avoid running an antenna system ground conductor into or through a building. In the unlikely event of a direct lighting strike or major power system fault, it seems prudent to at least try to keep the energy outside the building.
The option of running a #10 or better mast ground direct to the existing electrical service ground and avoiding the expense of a new rod and #6 copper looks like the best choice to me.
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