Thanks for the reply. Sorry for getting back to you so late. Other, more pressing problems have cropped up with the phone in the mean time.
To address your suggestions:
1) I don't know exactly what you mean by testing multiple wi-fi networks. If you mean try to be on other wi-fi networks while trying to use the Play Next option to see if it functions any more correctly, a) I also have this same problem with downloaded music so I don't understand how a different wi-fi network would affect the play order, and b) if it did work on other wi-fi networks, I'd still have the problem of it not working on my own wi-fi network, which would still be an issue.
2) I've had this issue with both not-downloaded as well as downloaded music. (And this frankly would remain a problem if it didn't happen with downloaded music but still did with non-downloaded music, as I don't want to have to download everything I want to listen to on the spur-of-the-moment.)
3) I may give this option a shot, but to clarify, would I need to do this for every time I want to use Play Next on a particular track? And if not each time, just the once to try out the result?
4) See #2 above (i.e. I've had this issue with non-downloaded as well as downloaded songs, so it doesn't seem to be dependent on whether or not it's in my library).
5) None of these have been purchased. It's all purely issues while streaming or playing downloaded playlists.
If it helps narrow anything down, the last time I tried to use a Play Next insertion in the middle of a song (with a downloaded track), it stacked the requested song four songs later. Meaning, it wasn't the next one set to play (as one would expect), nor the one after that, but was put into the upcoming playlist four songs after the one that was currently playing.
Any further suggestions would be much appreciated.