Entity reference field hidden widget or edit disabled on custom form

I have a custom node creation form I am rendering within a views preprocess hook. In that form I have two entity reference fields. I am setting the [#value] and [#default_value] of those reference fields programmatically.

On form submit the values I've set are created, but only if the fields are "editable" by the user. I want to make the fields "disabled" and/or "hidden" from the user. Not just hidden with CSS but with the entire autocomplete widget being made inaccessible. The field needs to be type "hidden".

How can I make an autocomplete entity reference disabled and/or inaccessible to the user creating the content?

Or another way of putting it, how can I add entity reference values programmatically on form submit without the user being able to interact with the fields?

Here are some things I've tried that do not work:

1. $form['field_entity_reference']['#access'] = false; // Setting #access to false seems as though it should work because the form fields still exist when debugging $form, but it does not work as it prevents the value from being submitted.
2. Adding ['#attributes']['readonly'], changing ['#type'] to hidden or another widget type, adding ['#attributed']['disabled']. None work
3. Entity prepopulate - This does not work for this particular situation as some values cannot be provided by tokens

Code for reference

function <theme>_preprocess_views_view_field(&$variables) {
  $view = $variables['view'];
  
  if ($view->id() == '<view>') {
    $field = $variables['field'];

    switch($field->options['id']) {
      case '<view_field>':
        $node = \Drupal::entityTypeManager()
          ->getStorage('node')
          ->create(['type' => '<node_type>']);
        $form = \Drupal::service('entity.form_builder')->getForm($node, 'secondary');

        // Set default_value and value
        $form['field_entity_reference']['widget']['#default_value'] = (int)$cid; // Note this is using the "select list" widget for the entity reference field
        $form['field_entity_reference']['widget']['#value'] = (int)$cid; // Same as above

        // Stuff that doesn't work. Values do not submit unless field is editable by user, or the field is not hidden/disabled
        $form['field_entity_reference']['#access'] = false; // Value does not submit
        $form['field_entity_reference']['widget'][0]['#attributes']['readonly'] = 'readonly'; // Doesn't make field read only
        $form['field_entity_reference']['widget'][0]['value']['#type'] = 'hidden'; // Seems autocomplete widget and select widget do not have a "hidden" type
        $form['field_entity_reference']['widget'][0]['target_id']['#type'] = 'textfield'; // Seems one cannot change the type to textfield

        // Change view field output to the form
        $variables['output'] = $form;
      break;
    }
  }
}

Kudos to @Patrick Kenny for setting me on a workable path with hook_entity_presave(). I'm posting this as an "answer" as it provided a means of accomplishing what I needed, but I still think the D8 entity reference field is missing a "hidden" widget type. Perhaps a port of entityreference_hidden. If anybody knows how to accomplish that programmatically please share.

Here’s how I accomplished what I needed.

1. Create a redundant integer field on the content type to hold value which will be applied to the entity reference field once hook_entity_presave() runs.
2. Set the redundant integer field to be available on the form, change the field type to hidden. You can use the field_hidden module for this.
3. Inside the theme hook_preprocess_views_view_field() hook set the value of the redundant field to the target node id (see code in original question to understand what I mean here). Note this is just for my example as I am adding the form to a views row specific field, but could be applied in other hooks.
4. In a custom module, inside hook_entity_presave() grab the redundant field value and apply it to the entity reference field before save (see code below)

function <module>_entity_presave($entity) {
  if ($entity->getEntityType()->id() == 'node') {
    if ($entity->bundle() == ‘<content_type>’) {
      // ----- Get entity id
      $eid = $entity->redundant_field_name->value;
      
      // ----- Set entity field target_value
      $entity->normal_entity_reference_field>target_id = $eid;
    }
  }
}

A side note about hooks within the <theme>.theme file

The hook_form_alter() hook when within the <theme>.theme file do not always apply in the way/order in which one might hope.

For example applying [#ajax] to a form action does not make that form ajax capable unless the hook is within a module (theme file hooks will not work). It appears this is because the application of necessary form configuration happens before theme hooks are run.