Maybe then, some kind of apprenticeship might work? Since there are those problems you mentioned, maybe some kind of Stacy-based apprenticeship. Classes on more general subjects of the different departments, and as one of the kids gets older and more interested in a particular department, their apprenticeship is taken up by that particular department.
For example, let's say Devlin's learning general stuff about the various departments. Who they are, what they do, and some of how they do it--though definitely not the really in-depth stuff. Like, small-scale inventions/repairs in Engineering or some first aid for Medical or biology or chemistry for Science. After a while spent learning, he says he's really interested in Medical, so he starts learning there as a sort of on-the-job training basis, and he watches and practices on skills appropriate to his age (example: No brain surgery at eleven. Helping to treat a broken bone, okay).
Re: NEW DEPARTMENT SUGGESTIONS/MISCELLANY
For example, let's say Devlin's learning general stuff about the various departments. Who they are, what they do, and some of how they do it--though definitely not the really in-depth stuff. Like, small-scale inventions/repairs in Engineering or some first aid for Medical or biology or chemistry for Science. After a while spent learning, he says he's really interested in Medical, so he starts learning there as a sort of on-the-job training basis, and he watches and practices on skills appropriate to his age (example: No brain surgery at eleven. Helping to treat a broken bone, okay).