I think that two very different accents are being discussed here. One is the Great Gatsby upper class private schooled 1920’s New Englander who wish they were aristocrats and have a pseudo-posh British accent going. I had an elderly Greek history professor with this very accent, and it drove me up the wall.
The other is the streetwise 1930’s New York reporter who sounds like no real person I have ever heard, in New York or elsewhere. This accent appears to only exist in the mind and mouths of actors playing low level gansters or guys wearing a fedora with a little tag saying PRESS tucked into the band. The best I can describe it is try taking Moe Howard’s accent, over-enunciate, and speed it up.
I’m going to try to track down some audio links to both so people who don’t get it can hear. I can atest that the upper-crust accent was real, because I’ve heard real people use it. The “reporter” accent, however, is another story. Has anyone ever heard a real person speak like this? Maybe a retiree in Florida?