The pronunciation with /-z-/ is unknown to both LPD and CEPD.…and, I might add, to all other reference books I have to hand — with one exception. That exception is the Oxford Dictionary of Pronunciation (alongside), which comes from the same stable as the OED.
My gut feeling is that it’s pretty bizarre to claim that Americans (or anyone else) typically pronounce nzt rather than nst in monstrous, particularly since no z pronunciation is suggested for the base form monster. It looks to me more like an individual idiosyncratic mislearning of the pronunciation of a particular word.
Looking further into ODP, however, I find that that doesn’t seem to be the case. In that dictionary AmE z variants, always prioritized, are given not only for monstrous but also inter alia for inscription, inscrutable, inscribe, inspire, instant, instinct, institute, instruct, instruction, instrument and monstrosity. As I say, there is no such variant suggested for monster, nor for demonstrative or demonstrate, nor (for example) for constable, constellation, constipation, constitution, constant, gangster, hamster, inspiration, instructive, instructor, seamstress.
As you can see, I have examined an assortment of words in which the usual pronunciation has nasal plus s plus plosive. But as far as I can see there doesn’t seem to be any consistency in this matter. Do people really treat monster differently from monstrous, inspire differently from inspiration, instruct differently from instructor?
I wonder if Bill Kretzschmar, the author who presumably contributed these pronunciation entries, would care to comment.
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Happy Easter, everyone. Next posting: 26 April.