The Dreaded Recently Added Folder - iPhone Music Player

I know it's not a new thread, but worth a shot to ask.

There are songs listed in the Recently Added folder of my iPhone (11.3) Music Player that are not downloaded to the device (by choice - for space saving and because I simply don't want them there). When my car or other bluetooth devices are in shuffle mode playing from my iPhone they all attempt to play these songs because they are listed in the Music player, and naturally my car doesn't know they are not actually downloaded. My car stereo either times-out or has extended pauses between songs, and after 10 or 12 attempts to play songs that aren't there the stress levels start to go through the roof.

The only option the iPhone Music player provides is to 'Delete From Library', but I don't want it deleted from my library (i.e. all devices), I just want these song titles off my phone.

I do not use Apple Music, I do not have 'auto-download other purchases' selected, and there is no way I can get rid of the songs listed in the Recently Added folder.

Streaming via bluetooth from my phone in my car is near useless at present.

Any suggestions?