Yes, if you want to combine an NZ flight with a *A flight in a single booking/ticket then the NZ sector must come from the *A redemption booking class - X. So, X + I is correct. Alternatively you could book two separate tickets, but if the connection is tight then I wouldn't recommend it.
SQ - I booked SIN/AKL on SQ in F using the online booking portal on 12 September this year. About a week or so later there were no SQ seats to be found via the online portal. I haven't heard any reasonable reason for this yet. As you say plenty of SQ award availability via AS and other *A carriers.