Howdy creativetruth! Yes, Betty explained to the researchers that she abbreviated what she thought was New York being said.
I haven't read that they sent any airplanes out to look for her, I know they had several ships that went out, but I don't think they knew how far off course she was. Back in the 30's I don't think they had planes in use that were designed as search planes.
That's a good point about the military not wanting to admit that a regular civilian radio could pick up what their radios couldn't! There definitely could have been some efforts not be embarrassed which could mean a coverup. Great points creativetruth, thank you!