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I would drive a ground rod down at the out building and ground both the RG6 and mast there to the same grounding rod.
You are protecting from a spike from lighting, keeping it away from your house instead of running it into your house would be the better course to take.
And ideally your panel at the shop should also have it's own ground at the shop instead of using the one in the house, for the same reasons.
Edit, how is the RG6 being run to the house? In the same conduit as the electrical? That may create interference issues if so.
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