can explain to clients that PageSpeed score is by no means the be->all and end-all

You're wrong here. While I do agree w/ that PageSpeed itself does not matter much but one should remember that most of the clients run businesses and they want to be known by others via Google. ONe likes or not but PageSpeed is one of the factor ranks well.

The total load time is 12.4s, which is high, but everything is visible, >usable, and to the end user, done at 1.8s, which is fairly >respectable. ( < 2s target time), on first load.

Mate, You gotta need to do a bit of research how companies lose millions on each second delay. I checked the source of the page and I can see he is using multiple CSS and JS files. He's also using uncompressed images. All these things can be optimized by merging files and minimizing them. Automation tools like gulp already available. Such small tweaks improve performance a lot. While he's not taking care of such things for his own site then he'd be doing same mistake on clients website as well.

I did not criticize his work, he made good things. Only he if speeds them up he would be able to get more clients.