It looks like I don't understand the use of 'next' in this context,

Yes. 'next' means "exit the block I'm in now, and skip anything (other than a continue block) afterwards." Every time you called 'next', your program skipped directly to the next iteration of the loop without going any further - in your original program, that's why only the

        my $name = $connect->quote($_);
        next;
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parts of the loop were being executed.