What kind of locking/transaction isolation level is appropriate for this situation?

Only in serializable isolation level MySQL won't allow you to read the rows that are being modified by another transaction. In any lower isolation level, you will see the rows in the state they were before the transaction, that modifies them, have been started. Of course, in READ_UNCOMITTED, the rows will be seen as deleted / modified, although transaction hasn't been completed.

You can use locking of tables to prevent this. Check this for more info on lock tables.

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