Just to add my recent personal experience:
there are only 3 options when u call to the DGAC:
1st (and most common): they don't answer the phone
2nd (quite common too): number busy, of course they are not using it, just lift the phone to avoid annoyances...
3rd (very helpful!): "no, it's not here, you have to call to this number..." where obiously you'll have these 3 options again!
The worst is that when you get to talk to someone they treat you like !!!!, I would strongly recommend you, as someone above, to convert your licence to an UK or Irish one ASAP!
Good luck!