Still, I think you're right to say it'll probably be simpler to go the normal route as the American spouse of a British citizen - not least because acquiring new citizenships can have unpredicted new obligations.
I think that's right. To answer Aviatrix's point above, the UK authorities wouldn't object to your using your Irish nationality (once you could prove it), but in the long-term I think it's better to do it the "regulation" way: as I say, for one thing it would simplify significantly the requirements that she would have to fulfil if she were to want to naturalise as a British citizen in the future — that's as things stand now, and even if the mooted changes to immigration/nationality law were to take effect, it is likely that spouses of British citizens will still have easier access to naturalisation than spouses of citizens of other EU countries.
On the whole, the granting of spouse visas to people in your sort of position is usually fairly straightforward and reasonably quick.
One other point to consider, perhaps: are you eligible for naturalisation as a US citizen, and if so have you thought about doing that? Once you cease living in the US, your residency rights there become precarious, at best, whereas if you were a US citizen you could of course return at any time. There are certain obligations that US citizens must meet (most notably the filing of annual tax returns — not the same thing as saying that all US citizens resident overseas are liable for US tax), but for most people these are not onerous. You would not need to give up your British citizenship if you did this (as, indeed, your wife would not need to give up her US citizenship if she were to become a British citizen in the fullness of time). Anyway, just a thought.