@Loh Jane,
The word "regardfully" sounds like the name of a song that would be the signature song of a new Broadway musical. It would have to have a meaning that would only apply to the musical's story line. Perhaps, someone was not yet able to speak English correctly, and used the word "regardfully," and then the musical's cast would break into song, with the word "regardfully" being repeated a number of times in the song. In effect, shades of "The rain in Spain falls mainly on the plain." (My Fair Lady.)