I have accounts in the same branch as you and have had similar problems. My employer was able to pay salary no problem, but had difficulties paying expenses which came from a different system.
I had a bit of a heated discussion with Finance when I pointed out that I would rather believe Bank of Ireland than them. After all BOIs business revolves around getting the correct money into the correct account using IBANs and account codes.
It all came down to a poorly written application on our end which said country id plus bank identifier plus sort code plus account number plus check equals IBAN when this is not necessarily the case. It is the case 90%+ of the time, but the standards do not dictate that this must be so . . . I checked.
So, the key thing is that your IBAN could be IEBOFILIKETOEATBANANAS and the money would get through to you as long as BOI have an internal mapping from that IBAN to your account.
Also . . . your IBAN as advised to you by BOI (and on your statement) is correct, so don't waste more time trying to get them to confirm it, waste the time telling your employers their payment system needs to be fixed.
z