Phile0124, thanks the VLC advice. However, VLC cannot see the folder under Files to which the files have been uploaded (and under which they will indeed play on an individual basis). I was able to get the files into Dropbox, but while VLC can connect to Dropbox, when I get down to where the actual MP3 files are, VLC says "no supported files".
I have noticed in reading recent reviews of a number of music players and file-manager type apps that many have undergone recent updates under which users can no longer see separately-downloaded media files and/or have seen that the apps are suddenly become much more limited in terms of the folders/directories they can access in general. One gets the impression that "someone" is pressing these developers across the board to limit functionality in order to more tightly control operations of the type I (and many others, seemingly) are trying to do.
I appreciate the advice here, and it has been an interesting few hours of learning, but not having something as simple as a universal file/directory browser, quite apart from the MP3 issue, seems like a crippling limitation of iOS currently, and one that has been done for some sort of corporate or DRM benefit, not mine. Too bad, since overall I feel iOS has the edge for look and feel, but I prefer not to be hogtied in this manner.