Aha, I have made some progress. I have it going for admin/invoice.php, with this code at line 150:
<td class="main"><?php echo $order->info['payment_method'] . " (" . $order->info['cc_type'] . " " . $order->info['cc_number'] . ")"; ?></td>
Look OK?

However, making a similar change to admin/orders.php seems deeper... I'm not sure where to make the change so the info shows up in the right-hand column summary of an order.

Pointers appreciated!