Just set up a function that prints to both screen and to the log file. Use that function when you want it to be logged; use regular print if it's the progress messages.

sub dPrint {
    my ($text, $handle) = @_;

    print $text;
    print $handle $text;
}
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Alternately, just do ....... until it finishes. Maybe one . per 5% or a certain number of records or whatever?