Not quite matching your spec but here you go. I implemented as much as I would use...

my %path;
my ($high, $low) = (0,0);
for (split /:/, $ENV{PATH} ){
  next if exists $path{$_};   # remove duplicates
  $path{$_} = $high;
  ++$high;
}

for (@ARGV){
  /^-(.*)/ and do {delete $path{$1} if exists $path{$1}; next;};
  /^\+\+(.*)/ and do {--$low; $path{$1}=$low unless exists $path{$1}; 
+next;};
  /^\+(.*)/ and do {++$high; $path{$1}=$high unless exists $path{$1}; 
+next;};
}

print join ":", sort {$path{$a} <=> $path{$b} }  keys %path;
print "\n";
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