HomePod skips songs on playlist played from Music on my iPhone

I have an iPhone 12 Pro (iOS 18.7.1), and several HomePods (all running 26.0.1). I have a large music collection of files that I own. I play these on my iPhone by transferring the files to the iPhone, then playing in the Music app. I also have an Apple Music subscription that I use from time to time, but I primarily listen to playlists of files that are copied to my phone.

I'm running into a problem on playlists where I have a mix of files purchased from iTunes and files from other sources, particularly files from rare sources that are not available in Apple Music (ex., recordings of my choir's performances). If I start playing the playlist on one of these rare files, then cast to my HomePod, the playlist plays with no issues. If I start playing a song I purchased from iTunes, then cast to my HomePod, I can see the queue in the app clear then repopulate--and now it only contains the songs I purchased from iTunes, and won't play the other songs at all. My guess is that the HomePod is trying to stream from Apple Music rather than just playing what's on my phone.

How do I fix this? How do I get it to play all the songs in the playlist?

(I'm also having a separate issue where some tracks will play on iTunes on my computer but won't play on either my iPhone or the HomePod.)