I've got a partial solution—it does what I want (I think), but takes several queries to do it. It's based on the node I linked above. Here's what I have:

    my $attrs   = {
        order_by => "$order DESC",
        page => $page,
        rows => $rows,
        columns  => [ qw(title title_norm description created modified
+ status 
                         rating owner.nickname owner.nick_norm ) ],
        join => [ qw(owner) ],
    };
    
    my $articles = $c->model('DBIC::Articles');
    
    # Build the query.
    if($owner) {
        $articles = $articles->search({ owner => $owner });
    }
    if(@with) {
        $articles = $articles->search_related('taglinks', 
            {
                tag => { -in => [ @with ] }
            },
            {
                select   => [ 'article', { count => '*' } ],
                group_by => [ 'article' ],
                having   => [ 'COUNT( * )' => scalar(@with) ]
            }
        )->search_related('article');
    }
    if(@without) {
        my $excluded = $articles->search_related('taglinks',
            {
                tag => { -in => [ @without ] },
            },
            {
                columns  => [ 'article' ],
                group_by => [ 'article' ]
            }
        );
        if($excluded) {
            my @excluded_ids = map { $_->id } $excluded->all;
            $articles = $articles->search(
                { id => { -not_in => \@excluded_ids } }
            );
        }
    }
    $articles = $articles->search(undef, $attrs);
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