I am not a professional, just a struggling older worker. My advice is persistence pays on these mixed UK/Irish state pension things. It took me 18 months to sort out my husband's. Long delays on the Irish side due to lack of resources, incorrect contributions record from the UK first time around which caused chaos. We were able to do some pension buy back from the UK. But eventually the letter I got was so confusing I thought that an almost-full UK state pension was being reduced by Ireland to 58 euros a week! In fact, when I managed to get them to explain the letter, that amount was the weekly top up from Ireland for his years working here, in addition to the separately-paid UK amount. I would estimate my time in sorting it all out at around 200 hours.
It is also worth knowing that there seems to have been a recent UK reorganisation. You can now only get a full copy of your year-by-year historical UK NI contributions from the tax people (HMRC) not the International pensions guys in Newcastle who only have a summary. I just got mine after 5 attempts on websites, in writing, on the phone, and it turns out they have lost 5 years contributions from the late 80s in the UK. I'm a person who still has cheque books from that period so I'm hoping I'll be able to get them back... Start early, keep all your documents well-filed, and persist...Best of luck!