Wordpress Frontend Create Post (custom post type) with file upload

Question

I am making a simple plugin that lets users add content to a custom post type. The frontend form includes a few text fields and a file upload field. I am using ajax to submit the form and it's working fine. However, I am trying to make the file upload field to work as well. Once the file has been uploaded, it's value (url) will be added as a custom field.

I am not that familiar with ajax and that's probably why my attempts so far were unsuccessfull. Below is the code I am using so far, minus the file upload stuff:

JS:

(function($) {

  $('.btn').on('click', function(e) {
    $('.btn').html('<i class="fa fa-spinner fa-pulse"></i>')
    e.preventDefault();
    var fname = $('#first-name').val();
    var lname = $('#last-name').val();
    var email = $('#email').val();
    var address = $('#address').val();
    var phone = $('#phone').val();
    var security = $('#security').val();
    //var file = $('#entryfile').files[0];

    // ajax the results!
    $.ajax({
      url: ajax.ajax_url,
      type: "POST",
      dataType : "json",
      contentType: false,
      processData: false,
      data: {
        action: 'entry_add',
        fname:fname,
        lname:lname,
        email:email,
        address:address,
        phone:phone,
        nonce: security,
        file:file
      },
      success: function( response ) {
        console.log( response );
        $('.contest-entry').hide('500', function() {
          $('.message > h2').html( response );
          $('.message').show('fast');
        });
      }
    });

  });

})( jQuery );

PHP:

function ajax_entry() {
  check_ajax_referer( 'add-entry-nonce', 'nonce' );

  $email = urldecode($_POST['email']);
  $fname = wp_strip_all_tags($_POST['fname']);
  $lname = wp_strip_all_tags($_POST['lname']);
  $addr  = wp_strip_all_tags($_POST['address']);
  $phone = wp_strip_all_tags($_POST['phone']);

  $success = "<i class='fa fa-check'></i> Thanks for joining! You will be reditected to step 2 in a few seconds";
  $error = "<i class='fa fa-exclamation-triangle'></i> Looks like something went wrong! Try again maybe?";

  if( !empty($email) && !empty($fname) && !empty($lname) && !empty($addr) ) {
    $postData = array(
      'post_title'  => $fname . ' ' . $lname,
      'post_type'   => 'contestants',
      'post_status' => 'draft'
    );
    $post = wp_insert_post( $postData );
    add_post_meta($post, "field_entry_unique", "WTH-".$post);
    add_post_meta($post, "field_first_name", $fname);
    add_post_meta($post, "field_last_name", $lname);
    add_post_meta($post, "field_email", $email);
    add_post_meta($post, "field_address", $addr);
    add_post_meta($post, "field_status", "pending");
    add_post_meta($post, "field_phone", $phone);

    if( $post != -1 ) {
      //echo json_encode($success);
      echo json_encode($file);
    } else {
      echo json_encode($error);
    }
  } else {
    echo json_encode($error);
  }
  exit;
}

Can you please help me find a way to make upload work?

EDIT: All solutions I came across so far either do not work (or I just could not make them work), require a second form or break the existing form, thus not allowing for the post to be created. I need some guidance (a few lines of sample code would be great too) as to how I can do this. jQuery is not my strength....

UPDATE: I managed to make this work by using the below. However, while logged out, the upload fails and the console logs a redirect to the login page. Any thoughts?

 var formData = new FormData();
      formData.append("action", "upload-attachment");
      var fileInputElement = document.getElementById("entryfile");
      formData.append("async-upload", fileInputElement.files[0]);
      formData.append("name", fileInputElement.files[0].name);
      formData.append("_wpnonce", upload_nonce);
      var xhr = new XMLHttpRequest();
      xhr.onreadystatechange=function(){
        if (xhr.readyState==4 && xhr.status==200){
          console.log(xhr.responseText);             
        }
      }
      xhr.open("POST","wp-admin/async-upload.php",true);
      xhr.send(formData);