I've read that new Residents cannot travel leave NZ for longer than 24 months - is that right? I've also read that they must be in the country for six months of each of those two years in order to qualify to apply for Permanent Residency thereafter.
That's about right. With Residence, you get two years travel conditions, allowing you to travel freely in and out of NZ. A minimum of two years after being granted Residence, if you have demonstrated commitment to NZ (and spending at least half of each year of the two prior to application is one recognized way of doing that), you can get PR. There are other criteria for demonstrating commitment, as shown here.
http://www.immigration.govt.nz/migra...quirements.htm
But I don't understand the exact implications of our plan - e.g. if we are allowed to go but she doesn't meet the criteria for PR thereafter, does she simply remain a New Resident until such time that she does qualify?
If she is back in NZ BEFORE the travel conditions run out, yes. Within NZ, Residence doesn't expire.
But being outside NZ with expired travel conditions would be to let her Residence lapse, so she'd have no special rights and would have to start applying all over again. For your idea to work would mean she would have to plan to be back in NZ in good time before the end of the travel conditions, to allow for travel delays (as the timing is absolute, and no excuse is any good). OR she would have to have applied and been granted an extension of her travel conditions - see under Special Categories, here.
http://www.immigration.govt.nz/migra...quirements.htm (I should add, I haven't heard of anybody who has gone through this last option, so I can't say how easily, or not, that goes through.)
Otherwise, as you'll see from that page, she would not have the option of travelling freely outside NZ for the following two years (or however much longer till she completed one of the conditions) - if she had spent very little time in NZ before her return, the longest renewal of travel conditions she would be able to get (before gaining PR) would be 14 days.