Postgres SQLSTATE[08006] [7] timeout expired

I have three servers behind a load balancer and a fourth server solely for Postgres 10 database that is not behind the load balancer. All four are behind the same firewall, with port 5432 open.

I have a simple browser-based html form to submit email addresses, usernames and passwords; the form submits through a jQuery program that calls a php program.

I can navigate the browser to the IP address of the server that hosts the Postgres database and submit records to the database with no problems. When I navigate to the site's URL (which goes through the load balancer), I always get "SQLSTATE[08006] [7] timeout expired" after a short delay -- in other words, no connection.

The php program is very simple:

<?php
echo 'Hello ' . htmlspecialchars($_POST["firstname"]) . '!' ;
echo PHP_EOL;

$dsn = vsprintf('pgsql:host=%s;port=%s;dbname=%s;user=%s;password=%s', [
'host' => 'xxx.xx.xx.xx',
'port' => '5432',
'dbname' => '[DBNAME]',
'user' => '[USERNAME]',
'password' => '[PASSWORD]',
]);

echo 'HTTP Referer ' . $_SERVER['HTTP_REFERER'];
echo PHP_EOL;

echo 'IP Address ' . $_SERVER["REMOTE_ADDR"];
echo PHP_EOL;

try{
// create a PostgreSQL database connection

echo "I'm here now";
echo PHP_EOL;

//ini_set("default_socket_timeout", 300);
$pdo = new PDO($dsn);
$pdo->setAttribute(PDO::ATTR_TIMEOUT, 300);

// display a message if connected to the PostgreSQL successfully
if($pdo){
echo "Connected to the database successfully!";
echo PHP_EOL;
}
}catch (PDOException $e){
// report error message
echo $e->getMessage();
exit();
}

$pdo = null;

?>

The echo messages are simply debugging progress messages for the browser's dev console.

The pg_hba.conf has these lines enabled:

pg_hba.conf:
host all [username] 0.0.0.0/0 trust
host all all 0.0.0.0/0 md5
host all all ::/0 md5
host all all all md5

The $_SERVER["REMOTE_ADDR"]; line shown in my PHP program above always comes back with the address of the load balancer.

I'm new to Postgres, so any help with this connection problem will be very appreciated. Thanks a lot.