I had a similar experience very recently, I applied on March 26th and estimated date was April 30th. After that date it started to move and once it went to May 9th as the estimated date then I tried to contact them as our travel date was May 30th.
Contacting them was difficult; for about 5-7 consecutive days I tried to call them but each time it said they were too busy, you could not even wait in a queue. I tried web chat and that was the same. In the end I think I found some link via boards.ie and this did place me in a queue, when I got to chat to someone it was not that productive in that they said you should not book a travel date until you receive your passport, etc.
I tried to ask if there was any process to escalate this as it was 35 working days since I applied. In the end he said he would add a note and he hoped we would get it before the 30th but it was not exactly a plan. In the end we did get them late last week so all was ok. This does not really help you but I suppose it shows that this might be the norm re waiting times. Just keep trying is all I can suggest.