@aodoherty
In my case, I've noticed that if you learn all the spells for their specialization, the Sages have started (sometimes? always?) giving the wrong answer and saying they don't know you instead of saying you've learned them all.
In the save where I have the most casters, I make all the kids do Friend of the World as teenagers and give them Incredibly Friendly, so maintaining a friendship with the Sages is really easy. The one exception was my loner Sim, who learned all the spells out of books and for the three that are only taught by the Sages, she took a Potion of Forced Friendship and used it to get the spells out of the Sages.
But yeah, if I get that "I don't know you" message, I look and see how many spells in that school they know, and/or have them practice that school of magic (which gives the correct error message).
(Also, I think they've started giving out those capstone spells a rank early, but I'm not complaining, I'll take it!)
Anyway: there's no tome for the top 3 spells; you have to go to the Sages. I've always found the Sages to be the fastest way to learn spells, but yeah, the error message is wrong and if I get it I go brew more Potion of Plentiful Needs or practice a different school of magic to boost XP and come back after level up. It's tempting to not do it with a full house, though, which it sounds like you have! so the tomes are a better option, but you'll have to ask for the last three. One of my Sims went to the Magic Realm every day from 8-3 while her little siblings were in school for that reason.
I've started moving out some of my newly YA casters onto an empty lot and having them go to the Magic Realm and never leave until they're Virtuosos. LilSimsie's Magic Realm Reno has beds, but you can also nap on couches or guzzle Potion of Plentiful Needs.