if you're playing Apple Music on the HomePod, using the player in the HomePod will get rid of some of the stuttering.
You can accomplish this with hand off, just get the music playing on your phone, and hold it next to a hompod, the audio should jump over to the player in the HomePod automatically.
for Apple Music, handoff should send it to the player. For other apps like Spotify, it should start playing over airplay.
Or if in the airplay menu, click control other speakers at the bottom, it will pop up a list of your devices, and you can select there. Once you've done this, your Apple Music app on the phone becomes a controller for the player in the homepod.
to tell how it's being played, look at the bottom of the screen in the music app... "iPhone -> living room" means it's using airplay, "Living room" means it's playing on the HomePod directly.