Many thanks all!
Replies are very comforting that this second, more senior and experienced installer knows a bit more than the first!
I was tempted to just tell them to surface mount the wire from one end of the property to the other to avoid any further faff, but it seems that their suggestion may do the trick whilst being safe, taking less time to sort, and preserving my clean walls.
I really have appreciated ALL of your help on this so much. It scares me to think how many people are put in danger/are ripped off without knowing it!
God bless the age of the internet and god bless you all.
Have an amazing week!
P