Trying to figure out the best logic to get a page title

Seems to me that you just need some simple PHP logic. If you have the HTML of the page you want to get the title from and the title is in the format of Something | Here here is how I would approach it. The following is just a quick example, it can be optimized to be a little speedier by not running the before() and after() functions unless they are needed.

//This should return "Using right" since only the right side contains a domain name.  The left side contains spaces and a domain name which is not a
//valid domain name to begin with so it wouldnt match.
$content = "Some HTML Here that contains the page title <title>Its a test.com | title.com</title>";
$title = between('<title>', '</title>', $content, FALSE);  //The false allows $content to contain HTML in it.  It's a security thing for drupal.
$left = trim(before('|', $title));
$right = trim(after('|', $title));

//If the left side of the | is a domain name, use it as the title.
if (is_domain_name($left))
{
   echo "using left";
   $title = $left;
}
else  //Otherwise if left wasnt a domain name, assume the right side was instead and use that.
{
   echo "using right";
   $title = $right;
}

//Set your node title to the title, or use hook_form_alter() to set it in a node edit form or something.
$node->title = $title;

//This is a small utility function that I've yet to port to parsing_api but am considering converting it to use parsing_api to make it easily extensible.  You should be able to use this as it is without much trouble, it's just a monster to read lol.
function is_domain_name($string)
{
   return preg_match("/^([a-z0-9]([-a-z0-9]*[a-z0-9])?\\.)+((a[cdefgilmnoqrstuwxz]|aero|arpa)|(b[abdefghijmnorstvwyz]|biz)|(c[acdfghiklmnorsuvxyz]|cat|com|coop)|d[ejkmoz]|(e[ceghrstu]|edu)|f[ijkmor]|(g[abdefghilmnpqrstuwy]|gov)|h[kmnrtu]|(i[delmnoqrst]|info|int)|(j[emop]|jobs)|k[eghimnprwyz]|l[abcikrstuvy]|(m[acdghklmnopqrstuvwxyz]|mil|mobi|museum)|(n[acefgilopruz]|name|net)|(om|org)|(p[aefghklmnrstwy]|pro)|qa|r[eouw]|s[abcdeghijklmnortvyz]|(t[cdfghjklmnoprtvwz]|travel)|u[agkmsyz]|v[aceginu]|w[fs]|y[etu]|z[amw])$/i", $string);
}

Interesting, I like puzzles like this. Try this instead then:

   $content1 = "Some HTML Here that contains the page title test.com <title>Its a | testgwcomeg345345@#$!%#$%T^t|title.com</title> more stuff here";
   $content2 = "Some HTML Here that contains the page title test.com <title>Its a | testgw.comeg345345@#$!%#$%T^t|title.com</title>more stuff here";
   $content3 = "Some HTML Here that contains the page title test.com <title>Its a | testgwcomeg345345@#$!%#$%T^t|title.com more stuff here";
   $content4 = "Some HTML Here that contains the page title test.com <title>Its a | testgw.comeg345345@#$!%#$%T^t|title.com more stuff here";
   $content5 = "Some HTML Here that contains the page title test.com <title>Its a | testgwcomeg345345@#$!%#$%T^t|title.com</title>more stuff here";

   $domain_names[] = parse_domain_name_out_of_title($content1, $include_bad_title_tags = FALSE);
   $domain_names[] = parse_domain_name_out_of_title($content2, $include_bad_title_tags = FALSE);
   $domain_names[] = parse_domain_name_out_of_title($content3, $include_bad_title_tags = TRUE);
   $domain_names[] = parse_domain_name_out_of_title($content4, $include_bad_title_tags = TRUE);
   $domain_names[] = parse_domain_name_out_of_title($content5, $include_bad_title_tags = TRUE);

   print_r($domain_names);
   /*
      The resulting array will look like this:
      Array
(
    [0] => title.com
    [1] => testgw.com
    [2] => title.com
    [3] => testgw.com
    [4] => title.com
)
   */


//This function returns the FIRST domain name that it finds in a <title>.
function parse_domain_name_out_of_title($string, $include_bad_title_tags = FALSE)
   {
      if ($include_bad_title_tags)
      {
         $title = after('<title>', $string);
      }
      else
      {
         $title = between('<title>', '</title>', $string, FALSE);
      }

      //Normal domain names for the US/CA
      $domain_extensions[] = '.us';
      $domain_extensions[] = '.ca';
      $domain_extensions[] = '.com';
      $domain_extensions[] = '.net';
      $domain_extensions[] = '.org';
      $domain_extensions[] = '.gov';
      $domain_extensions[] = '.biz';
      $domain_extensions[] = '.tv';
      $domain_extensions[] = '.info';
      $domain_extensions[] = '.edu';
      $domain_extensions[] = '.mil';

      //Oddball domain names
      $domain_extensions[] = '.aero';
      $domain_extensions[] = '.asia';
      $domain_extensions[] = '.cat';
      $domain_extensions[] = '.coop';
      $domain_extensions[] = '.int';
      $domain_extensions[] = '.mobi';
      $domain_extensions[] = '.museum';
      $domain_extensions[] = '.name';
      $domain_extensions[] = '.pro';
      $domain_extensions[] = '.tel';
      $domain_extensions[] = '.travel';
      $domain_extensions[] = '.xxx';

      //Country level domain names (To many to list here, add as needed.)
      $domain_extensions[] = '.uk';
      $domain_extensions[] = '.jp';
      $domain_extensions[] = '.cn';
      $domain_extensions[] = '.au';

      foreach ($domain_extensions AS $key => $extension)
      {
         $domain_name_prefix = before($extension, $title, FALSE);

         //We have a possible domain name hit
         if ($domain_name_prefix)
         {
            //Check to see if there are any spaces first, if so, then it should be the LAST space where the domain name resides.
            if (strstr($domain_name_prefix, ' '))
            {
               $domain_name = after_last(' ', $domain_name_prefix.$extension);
            }

            //Make sure the first character is alphanumeric.  If its not, strip it off and re-test.  This will knock out any unknown non-alphanumeric
            //separators that may be in use such as | symbols.

            $size = strlen($domain_name);

            while($size--)
            {
               //The only non-alphanumeric chars in a domain name will be . and - so we check for those first.  Then check for alphanumeric.
               if ($domain_name[$size] != '.' && $domain_name[$size] != '-' && !ctype_alnum($domain_name[$size]))
               {
                  $domain_name = after($domain_name[0], $domain_name);  //Knock off the first character in the string.  This works because all strings are also an array.
               }
            }

            if ($domain_name && is_domain_name($domain_name))
            {
               //Houston we have a domain name, stop here and return it :D
               return $domain_name;
            }
         }
      }
   }
   //This is a small utility function that I've yet to port to parsing_api but am considering converting it to use parsing_api to make it easily readable.  You should be able to use this as it is without much trouble, it's just a monster to read lol.
   function is_domain_name($string)
   {
      return preg_match("/^([a-z0-9]([-a-z0-9]*[a-z0-9])?\\.)+((a[cdefgilmnoqrstuwxz]|aero|arpa)|(b[abdefghijmnorstvwyz]|biz)|(c[acdfghiklmnorsuvxyz]|cat|com|coop)|d[ejkmoz]|(e[ceghrstu]|edu)|f[ijkmor]|(g[abdefghilmnpqrstuwy]|gov)|h[kmnrtu]|(i[delmnoqrst]|info|int)|(j[emop]|jobs)|k[eghimnprwyz]|l[abcikrstuvy]|(m[acdghklmnopqrstuvwxyz]|mil|mobi|museum)|(n[acefgilopruz]|name|net)|(om|org)|(p[aefghklmnrstwy]|pro)|qa|r[eouw]|s[abcdeghijklmnortvyz]|(t[cdfghjklmnoprtvwz]|travel)|u[agkmsyz]|v[aceginu]|w[fs]|y[etu]|z[amw])$/i", $string);
   }