I think you forgot that learning skills changes scale as the rating goes up (quite drastically).
Raising a skill from 9 to 10 takes 20 weeks. Which would be 140 days by itself.
Using the proper times, to go from Rating 4 to Rating 10 would take a total of 64 weeks. And on top of that, there is also the restriction that you can only increase a skill three times in a single downtime. So you would need to take a "break" from training at some point in there. Not to mention the karma to train that skill that many times. So we're talking probably a year and a half of intense training in that one single skill. Remember that many professions don't require singular training. You need to learn a variety of skills to be properly trained in a vocation of some sort.
To answer the OP, I would say that to buy off Uneducated would require the character to go through some sort of process to familiarize themselves with all of the sorts of skills that Uneducated represents as being "innately unfamiliar." This could mean taking some classes (either formally or by fellow runners), getting some intensive training, or some other method that the player can come up with. Be creative, you're buying off a pretty hefty quality (in terms of effect at least), it should have an effect on how your character acts and reacts to the world.