I want to change the source order of the "Create new account"/"Forgot your password?" links and the Submit button, so the Submit button comes first.

I am able to modify certain contents of the login block by using this function.

function THEMENAME_form_user_login_block_alter(&$form, &$form_state){
  $item = array();
  if (variable_get('user_register', USER_REGISTER_VISITORS_ADMINISTRATIVE_APPROVAL)) {
    $items[] = l(t('Create new account'), 'user/register', array('attributes' => array('title' => t('Create a new user account.'))));
  }
  $items[] = l(t('Request new password'), 'user/password', array('attributes' => array('title' => t('If you forgot your password, click to request a new password via e-mail.'))));
  $form['links']['#markup'] = theme('item_list', array('items' => $items));
}

And this template does pick up the changes and allow for markup changes around the form, but simply outputs the form in one variable. How do I modify the $content variable and print each element out separately to swap item locations?

block--user--login.tpl.php

<div id="user-login-top">
  <?php print render($title_prefix); ?>
  <?php if ($block->subject): ?>
    <h2<?php print $title_attributes; ?>><?php print $block->subject ?></h2>
  <?php endif;?>
 <?php print render($title_suffix); ?>
</div>
<div id="user-login-block" class="block block-<?php print $block->module ?>">
  <div class="content"<?php print $content_attributes; ?>>
    <?php print $content ?>
  </div>
</div>
<div id="user-login-bottom" class="block-bottom"></div>

This example uses straight markup out of Firebug and it does function, but there should be a cleaner way to do this by printing variables that already contain the markup, and that doesn't remove the "Create new account" option if the site registration is restricted.