No need to apologise! I have left him for 30 min before he starts crying (he escalates quickly once he starts) and I go in to calm him and he will almost always fall asleep almost as soon as he stops crying - I assume it's because I'm patting/rubbing his back to calm him. If I go in after 5 - 10 min and start patting him, he will also generally go off to sleep. Also, if he isn't asleep, as soon as I leave the room he's sitting up.
We've been doing nurofen, because we've found the same thing! Have not tried books yet, so will get DH on to the books.
Enjoy your break from the teeth! It seems unnecessarily nasty to me. I had my wisdom teeth moving around when DS's first 2 teeth came through. I have so much sympathy for the poor little things. 4 at once seems excessive, my poor kiddo.
I'm glad you've got the sleep sorted! It gives me great hope!