How to render a Commerce pane programmatically?
Panes are forms. Run them through drupal_get_form but you'll need to pass in some extra options:

require_once drupal_get_path('module', $payment_pane['module']) . '/' . $payment_pane['file'];
$order = commerce_order_load($order_id);
$payment_form = drupal_get_form($payment_pane['callbacks']['checkout_form'], $payment_pane, $order);
$output = drupal_render($payment_form);