I believe this process has changed significantly from what is in this article. Spoken and Written are now much more separate, with each having 3 separate levels of lessons and a final exam. I think the costs were 40, 60, 60, and 100 DjT for each exam (I think), which puts the cost of the entire process at 320 DjT. And Spoken/Written lessons can not be taken on the same in-game day. Which means (at minimum) it takes 8 Discworld days, or 3 Roundworld days.
And the lessons are a lot more useful than they used to be. You used to need, say, 40 Spoken Djelian for that third lesson, and it would raise your Djelian to 50. But if you were at 42 it would still only raise you to 50. Now it would raise your Spoken Djelian by 10, leaving you at 52, which feels A LOT nicer to the player grinding out language skills.
Sadly, I didn't see this page was so out-of-date when I re-did these lessons on my alt. So I did not record all the quest text for us to update this page.