Have them do the internal patch where they drill out/clean out the hole and put a rubber plug that is attached to a patch that stays internal. It wears at the same rate as the tire and since yours is not on the tread I doubt you will ever have an issue.
It wouldn't hurt the run-flat capability of the tire either.
Worse case is it doesn't hold air and you spend $20 to patch it. But if it does hold that is $400 you save.
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