Searching Papers Past, which is the New Zealand national digitised newspaper archive for 1929-30 found only two mentions of Mt Stevens.
The first, fairly straightforward on 22 June [Wellington Evening Post] said:
A mountain top at the head of the Anatoki Valley, in direct line with Kahurangi Point, and about 16 miles from Takaka, has not been visible since the big shock on Monday. (The mountain top mentioned is presumably Mount Stevens, 3950 feet high.)
With the magic of not-quite exact re-transmission this became by 6 August [Poverty Bay Herald, NZ]:
A United Press Association cablegram from London which circulated through the United States daily press on June 24 stated, with regard to the recent earthquake: “Mount Stevens, a New Zealand island, nearly 4000 ft. high, has disappeared because of earthquakes, according to a dispatch to the Daily Telegraph (London) from its Wellington correspondent, who quoted the postmaster at Takaka.
So what was probably haze obscuring of a distant peak, or perhaps a major scoria slide that reduced its height became the disappearance of Mt Stevens Island.
The whisper chain seems to be Takaka post-master [first report] -> NZ Evening Post -> London Daily Telegraph -> United Press ->US papers ->Local rag in Poverty Bay