real 3m21.523s ... real 1m24.273s

Nice, and subtle :)

Try this:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub dhm2int {
    my( $d, $h, $m ) = unpack '(A2)*', $_[0];
    return ( ( $d - 1 ) * 24 + $h ) * 60 + $m;
}

sub int2dhm {
    sprintf "%02d%02d%02d", int($_[0]/1440)+1, int($_[0]/60)%24, $_[0]
+%60;
}

my $tally = chr(255) x ( 31*24*60 );

while( <> ) {
    chomp;
    my( $sd, $ed, $v ) = split;
    my( $s, $e ) = map dhm2int( $_ ), $sd, $ed;
    while( int( $s / 1440 ) != int( $e / 1440 ) ) {
        my $newe = ( int( $s / 1440 ) +1 ) * 1440 -1;
        vec( $tally, $_, 8 ) > $v and vec( $tally, $_, 8 ) = $v
            for $s .. $newe;
        $s = $newe +1;
    }
    vec( $tally, $_, 8 ) > $v and vec( $tally, $_, 8 ) = $v
        for $s .. $e;
}

my @res;
my $i = 0;
while( $i < length( $tally ) ) {
    ++$i until vec( $tally, $i, 8 ) != 255;
    my $val = vec( $tally, $i, 8 );
    my $start = $i++;
    ++$i while $i % 1440 and vec( $tally, $i, 8 ) == $val;
    my $end = $i - 1;
    push @res, [ int2dhm( $start ), int2dhm( $end ), $val ];
}

pp \@res;
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