Interestingly enough, although Mrs NNH was born a US citizen, both her parents immigrated from Romania, so there is another potential EU mechanism for me to investigate.
Not sure what the situation is with Romania... new EU member states don't get full free movement rights for the first few years; don't know if Romania is past that stage yet.
If you don't currently have an Irish passport, and your wife doesn't currently hold Romanian citizenship, then it's probably just as easy to go the route originally suggested, i.e., apply for your wife to settle in the UK on the basis that she is the spouse of a UK national. The other two routes would probably involve similar amounts of bureaucracy.