You could try something like:

use constant READSIZE => ...;

my $fh = ...;
my $start = ...;
my $end   = ...; ## check $end < -s($fh)!

seek $fh, $start, 0;
while( ($_ = tell( $fh ) ) < $end ) {
    local $/ = \min( READSIZE, $end - $_ );
    my $chunk = <$fh> or die $!;
    ## ...
}
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