Getting list of Zoo Visitor entries with No Playa Parents and Solspace Super Search Result

Question

I'm trying to get a Super Search results loop that only displays entries with No Parents...

I'm currently pulling out all the results and just showing a label for the entries that don't have a Playa parent:

{exp:super_search:results channel="zoo_visitor" status="Members-id5|Members_Verified_-id6|Members_Pro-id7|open" orderby="date" sort="desc" limit="50" paginate="bottom" }

{if channel_name == 'zoo_visitor'}

    {exp:zoo_visitor:details} 

    <li>

      <strong>{mbr_formal_title} {member_firstname} {member_lastname} ({entry_id})</strong> 

      {exp:zoo_visitor:details}
      {exp:playa:parents channel="parents"} 

        {if total_results > 0}
            {title}
        {/if}

        {if no_parents}
            <span class="tip">No Parent</span>
        {/if}

      {/exp:playa:parents}
      {/exp:zoo_visitor:details}

    <hr>
    </li>

    {/exp:zoo_visitor:details}

{/if}  

<!-- Pagination Snippet -->
{_pagination}

{/exp:super_search:results}

Also happy to use default EE entries tag if it's easier / Super Search is causing the problem. Guessing it shouldn't make a difference though?

Edit (Response to question):

I tried this but it seems to spit out blank entries with parents...

{exp:super_search:results channel="zoo_visitor" status="open" orderby="date" sort="desc" limit="50" paginate="bottom" }

  {exp:zoo_visitor:details}
  {exp:playa:parents channel="parents"} 
     {if no_parents}
      <li> {mbr_formal_title} {member_firstname} {member_lastname ({entry_id})</li>
    {/if}
  {/exp:playa:parents}
  {/exp:zoo_visitor:details}

{_pagination}

{/exp:super_search:results}