Render page callback output in another region than "content"
Instead of defining a page via hook_menu it is better to define a block that you can place everywhere across the site.

Is there any requirement that restricts you to using a page?

If not the following code creates a block:

/**
* Implements hook_block_info().
*/
function YOUR_MODULE_block_info() {
  $blocks = array();
  $blocks['YOUR_BLOCK_ABC'] = array(
    'info' =&gt; t('YOUR BLOCK NAME'),
  );
  return $blocks;
}

/**
* Implements hook_block_view().
*/
function YOUR_MODULE_block_view($delta = '') {
  $block = array();
  switch ($delta) {
    case 'YOUR_BLOCK_ABC':
      $block['subject'] = '';
      $block['content'] = _YOUR_MODULE_BLOCK_ABC_CONTENT();
      break;
  }
  return $block;
}

function _YOUR_MODULE_BLOCK_ABC_CONTENT() {
  // This is where you code you use for the page goes.
  return t('Hello world');
}


Code from http://kahthong.com/2013/06/create-your-own-custom-drupal-block-programmatically

You can restrict the block visibility in the block settings to only be shown on single pages. Maybe this might solve the problem. To access arguments from the current page you can use the arg function.

Cheers
j