Re: the July voyage of the New York --
"The steamship New-York, Capt. WENKE, from Bremen on the 7th inst., calling at Southampton on the 10th, arrived here yesterday (July 24th).
Check the dateline of the newspaper clipping to which you refer. According to the NY Times, the 24 May reference is to the steamship New York arriving at Cape Race, Newfoundland. The Associated Press stationed a newsboat at Cape Race to meet ocean liners passing by on their way from Europe so that news could be telegraphed to New York.
I believe the New York arrived on 28 May, making the May crossing in roughly the same time as the July crossing.