As an aside, there are no other solutions of the form that Ton used (1x$&*XX where Ton's XX is 40). It seems that his solution truly is a one of a kind!

In addition to the one used in the 2006 Fonality golf challenge:

s!.!y$IVCXL426(-:$XLMCDIVX$dfor$$_.=5x$&*8%29628
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don't forget about Ton's original one (click on response by Ton Hospel) of equal length:

s!.!y$IVCXL91-80$XLMCDXVIII$dfor$$_.=4x$&%1859^7
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used in the 2004 Polish golf tournament. BTW I got a laugh out of this response by Maciej Misiak:

You should see some of Golfers after reading your explanation... eyes big like cups of tea, heart attacks, etc.

Update: Here is a test program to verify that all four magic formulae are correct:

use strict;
use Roman;

sub ton1 { my $t = shift; my $s;
($s.=4x$_%1859^7)=~y/IVCXL91-80/XLMCDXVIII/d
for $t=~/./g; return $s }

sub ton2 { my $t = shift; my $s;
($s.=5x$_*8%29628)=~y/IVCXL426(-:/XLMCDIVX/d
for $t=~/./g; return $s }

sub pmo1 { my $t = shift; my $s;
($s.="32e$_"%72726)=~y/CLXVI60-9/MDCLXVIX/d
for $t=~/./g; return $s }

sub pmo2 { my $t = shift; my $s;
($s.="57e$_"%474976)=~y/CLXVI0-9/MDCLXIXV/d
for $t=~/./g; return $s }

for my $i (1..3999) {
    my $r  = uc roman($i);
    my $t1 = ton1($i);
    my $t2 = ton2($i);
    my $p1 = pmo1($i);
    my $p2 = pmo2($i);
    print "$i: $r\n";
    $r eq $t1 or die "t1: expected '$r' got '$t1'\n";
    $r eq $t2 or die "t2: expected '$r' got '$t2'\n";
    $r eq $p1 or die "p1: expected '$r' got '$p1'\n";
    $r eq $p2 or die "p2: expected '$r' got '$p2'\n";
}
print "all tests successful\n";
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