I incline toward Tim here. Upon strike 3, batter is now a batter-runner, so he's out, return R3 to 3B. There's no 'time limit' on how long it takes the B/R to move toward 1B, so I can't see 'desertion' here.
If it were the same sitch except NOT strike 3, then its BI, batter remains at bat, R3 out.
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