How do I change the ID of a copy of an exposed filter? I'm using answers from Expose a view&#39;s filters both in a block, and in the actual view to duplicate an exposed filter as a block and make it appear in another region on every page.

I want to style both form copies a bit differently. When I started to look into the markup, I noticed that I'm getting two forms with identical IDs. Putting aside the styling, that's not good.
The code I am using is the following.

function MYMODULE_block_view($delta = ''){
  $block = array();
  switch($delta){
    case 'mysearch':
      $block['subject'] = t('My Search');
      $block['content'] = _MYMODULE_get_exposed_filter_form(); 
      break;
  }
  return $block;
}

/** Function to get the Exposed filter form **/
function _MYMODULE_get_exposed_filter_form(){
  $view = views_get_view('node_index_view');
  $view-&gt;set_display('page');
  $view-&gt;init_handlers();
  $exposed_form = $view-&gt;display_handler-&gt;get_plugin('exposed_form');
  return $exposed_form-&gt;render_exposed_form();
}


How do I alter the ID of the copied exposed filter block? If I use hook_form_alter() or hook_form_views_exposed_form_alter() it's going to apply the alteration to both instances.
This issue was discussed and answered in this thread, it includes a patch to fix the issue:

https://www.drupal.org/node/1735096

Another option is to use the module MEFIBS - More exposed forms in blocks