Rule schemes rarely have solutions for every referee mistake. The proper thing was to not blow the whistle and let the game end. Once the mistake of blowing the whistle is made, you're left with two choices. (1) Just give the DOG warning and keep going or (2) give a T (under either not-precisely-accurate-as-written theory). The latter is probably the most consistent with restoring the balance messed up by the whistle that should not have been blown.
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