I had a very similar problem on my Dell laptop, especially when running Audacity.
The snd-hda-intel model=dell-headset-multi
config looked promising but it didn't work. At first I thought I had solved it by reverting an update of alsa-utils. I went back from 1.2.2-1ubuntu2 to 1.2.2-1ubuntu1 using Synaptic Package Manager. This update came out a few days after your question so I guess my issue is not exactly the same as yours.
aplay -l
lists ALC3204
as my audio device in case someone needs this info.
When running alsa-utils 1.2.2-1ubuntu1, Audacity is kind of picky with audio devices but I can unplug and then plug my earphones in again to make everything work.
When running the 1.2.2-1ubuntu2 version however, plugging my earphones/headphones simply doesn't work. They are detected but no sound comes out. If I manage to get some sound (after rebooting a few times), then Audacity ruins everything leaving me with no sound on the 3.5mm jack again.
It seems that the problem manifests itself more clearly when booting with earphones plugged in and reconnecting the earphones while the settings app is open. Otherwise it might work correctly on either alsa-utils version, but 1.2.2-1ubuntu1 looks much more stable/predictable so I'm sticking to that version.