I feel like I’ve just made some progress, but maybe not!
I followed the links @Velgen posted and ended up at this post:
https://forums.linuxmint.com/viewtopic.php?p=1791086#p1791086
Which suggested making a change to /usr/share/pulseaudio/alsa-mixer/paths/analog-output-speaker.conf - this:
; This profile path is intended to control the speaker, let's mute headphones
; else there will be a spike when plugging in headphones
[Element Headphone]
switch = off
volume = off
to this:
; This profile path is intended to control the speaker, let's mute headphones
; else there will be a spike when plugging in headphones
[Element Headphone]
switch = mute
volume = merge
I made that change and rebooted. What I noticed then was the audio notification icon was muted with a red line through it. I double clicked on the notification icon, and then clicked the icon to unmute the line out channel:
I then had working audio from my lineout 
Going to try this now:
; This profile path is intended to control line out, let's mute headphones
; else there will be a spike when plugging in headphones
[Element Headphone]
switch = off
volume = merge
BRB…