Amazingly, yesterday afternoon I used my iPhone to order a passport card from the Irish Passport Office.
It took a total of about six minutes. Compare that to the standard paperwork these things require and even the time spent queuing for passports. This is going to be posted to my home address, so no requirement to do anything but wait.
Finally, government services catching up with 21st Century technology. Big thanks for the Department of Foreign Affairs for making it so easy for emigrants like me to access this service.