Here is a link to an article by Sherwood Goffin, examining the origin of the nusach yomim noraim; there are references to nusach of the Maharil
If you Google “nusach” and “Sherwood Goffin” you will find other articles, as well. This does not answer the Dovid haMelech question, but it begins to open a window on the origin of nusach. I’ll try to remember, but there is an authorative volume from the 1920s that traces many of the globally-common nusach ha-tefilos –