I did, of course, have my normal conversation with the salon when I booked the appointment:
Me: "Could you make it a double length appointment? My hair is *really* thick and always takes longer than normal to cut."
Salon Receptionist "Sure, that won't be a problem"
Stylist: "Wow, you have so much hair! It's really thick!"
Receptionist in background, to next customer "I'm afraid [Stylist's name] is running late - it'll be another 20 minutes or so.."
To do them justice, I didn't get any sense that the stylist then tried to rush to finish off my cut, but I felt a little sorry for the customer waiting an extra half hour because they didn't believe me..
Of course, now I shall spend the next few days combing the back of my neck, and using 3 times as much shampoo as I need, but on the whole I'm happy with the new look.