I don't know where the idea that the IAA "can't touch" N-reg aircraft or their pilots who hold FAA licences comes from. There is ample legal provision for prosecution of any pilot in breach of legislation.
In summary, S.13 of the Air Navigation and Transport Act of 1946 makes it an offence to be in breach of any order or regulation made under any order made under the Act. This Section has not been repealed since then (so far as I can tell) and thus remains the legal basis upon which any prosecution can be brought for any one of a number of offences arising from breaches of the various Orders and Regulations.
The Irish Aviation Authority has become empowered by the Irish Aviation Authority Act, 1993 as the responsible authority for the enforcement of legislation.
So, if we take Rule 2 of the Irish Aviation Authority (Rules of the Air) Order as an example -
Rule 2. Negligent or Reckless Operation
An aircraft shall not be operated in a negligent or reckless manner so as to endanger life or property.
The Rule (or the Order itself) doesn't say anything about the nationality of the aircraft or the licence of the pilot.
The only reason prosecutions haven't been taken against offenders for breaches of this rule (and many others) would seem to be simply because the IAA haven't done it - not because they can't do it.
Why not, I wonder?