How to make modal dialog submit buttons work when called with OpenModalDialog()?

Question

I'm having an issue with some modal dialogs in Drupal 8.3.5. My requirement says that when I'm on a particular form under a particular condition, then a modal dialog pops up and collects some additional information.

I can open the dialog, but I can't make the form actually do anything once it's up. Clicking the submit button doesn't actually fire anything on the server, but I do get "An AJAX HTTP error occurred".

The form itself is pretty simple:

public function buildForm(array $form, FormStateInterface $form_state, $options = NULL) {
  $form['#prefix'] = '<div id="modal_example_form">';
  $form['#suffix'] = '</div>';

  // The status messages that will contain any form errors.
  $form['status_messages'] = [
    '#type' => 'status_messages',
    '#weight' => -10,
  ];

  // A required checkbox field.
  $form['our_checkbox'] = [
    '#type' => 'checkbox',
    '#title' => $this->t('I Agree: modal forms are awesome!'),
    '#required' => TRUE,
  ];

  $form['actions'] = ['#type' => 'actions'];
  $form['actions']['send'] = [
    '#type' => 'submit',
    '#value' => $this->t('Submit modal form'),
    '#attributes' => [
      'class' => [
        'use-ajax',
      ],
    ],
    '#ajax' => [
      'callback' => [$this, 'submitModalFormAjax'],
      'event' => 'click',
    ],
  ];
  $form['#attached']['library'][] = 'core/drupal.dialog.ajax';

  return $form;
}

Here's the thing, though. When I open this form with a link, it works. When I open it with an OpenModalDialogCommand(), it doesn't.

The link that opens the form successfully and lets it submit:

$form['open_modal'] = [
  '#type' => 'link',
  '#title' => $this->t('Open Modal'),
  '#url' => Url::fromRoute('modal_form_example.open_modal_form'),
  '#attributes' => [
    'class' => [
      'use-ajax',
      'button',
    ],
  ],
];

And here is the OpenModalDialog() command that opens the form but doesn't let it submit:

function submitModalFormAjax(array &$form, FormStateInterface $form_state) {
  $response = new AjaxResponse();

  // Get the modal form using the form builder.
  $modal_form = \Drupal::formBuilder()->getForm('Drupal\modal_form_example\Form\ModalForm');

  // Add an AJAX command to open a modal dialog with the form as the content.
  $response->addCommand(new OpenModalDialogCommand('My Modal Form', $modal_form, ['width' => '800']));

  return $response;
}

Am I using the OpenModalDialog() wrong? Is there something I'm missing on my form to make it work correctly? Is there a different way I'm supposed to be calling the form?

How can I make my modal dialog submit buttons work when I call it with an OpenModalDialog() command?