OK I found a way to make it faster. The compromise is to trade speed for space... Instead of calling sort for every item that gets added to the list of the select few, I collect $workset extra items before doing the sort... That reduces the total number of calls to a relatively small number, roughly $workset times fewer calls. In my example code, with $workset = 100, I got just 3 calls total.

use strict;
use Time::HiRes 'time';
my %HASH;
foreach('AA' .. 'ZZ') {
    $HASH{$_} = 1 + int rand 1000;
}

my $t0 = time;
my @top;
{
    my $keep = 100;
    my $workset = 100;
    my $threshold;
    my $added = 0;
    while(my($key, $value) = each %HASH) {
        if(@top < $keep) {
            printf "Starting with %s => %d\n", $key => $value;
            push @top, [$key, $value];
        } elsif(not defined $threshold or $value > $threshold) {
            printf "Adding %s => %d\n", $key => $value;
            push @top, [$key, $value];
            if(++$added >= $workset) {
                printf "Shakedown from %d items\n", scalar @top;
                @top = sort { $b->[1] <=> $a->[1] } @top;
                $threshold = $top[my $i = $keep - 1][1];
                printf "New threshold: %d\n", $threshold;
                while($top[++$i][1] == $threshold) { }
                $#top = $i-1;
                printf "Keeping %d items\n", scalar @top;
                $added = 0;
            }
        } elsif($value == $threshold) {
            printf "Adding %s => %d\n", $key => $value;
            push @top, [$key, $value];
        } else {
            printf "Skipping %s => %d\n", $key => $value;
        }
    }
    printf "Final shakedown from %d items\n", scalar @top;
    @top = sort { $b->[1] <=> $a->[1] } @top;
    if(@top > $keep) {
        $threshold = $top[my $i = $keep - 1][1];
        printf "Final threshold: %d\n", $threshold;
        while($top[++$i][1] == $threshold) { }
        $#top = $i-1;
        printf "Keeping %d items\n", scalar @top;
    }
}

use Data::Dumper;
$Data::Dumper::Terse = 1;
print Dumper scalar @top, \@top;
my $t1 = time;
$, = "\t";
print $t1-$t0;
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