What's a simple & reliable way to transfer & listen to mp3s on my iPhone?
If you don't use Apple Music I would suggest something like iMazing (satisfied user for over a year) or another iTunes alternative with music management option. 

Another solution is using Infuse or VLC as a player instead of the native Music app, you can import songs with File Sharing in iTunes and it shouldn't be affected with the 'dotted circle' bug.