I get the idea of trying to optimize Jacob's skills as much as possible, but tbh I want to read a story about Jacob exploring the mysteries of Hogwarts and doing cool magic stuff, fighting monsters, figuring out mysteries, and making friends. So spending the next few months left in the term attempting to get 3 skills (Charms, Transfiguration, and Potions) that are already pretty good up to A+ (4 actions for each one assuming everything goes well) doesn't sound very appealing, especially when Jacob has many in-story reasons to focus on his weak areas like the Mind Arts and Understanding Creatures.
I guess what I'm trying to say is that for me personally story > mechanics. If it makes sense to train those subjects then I think we should do it, as long as doing so doesn't put a hold on Jacob's life and prevent him from actually enjoying it.
I understand your point in preferring story over min/maxing, but in Jacob's case I don't see there being an either/or when it comes to optimizing and his story. My assumptions were that we would use 6 personal actions per turn (which has been what we have had Jacob done at the least) and the classes I would focus on are the very ones that Jacob has had the most interest in and the ones we, as questers, decided that Jacob would be most interested in. Meaning that we would be spending 8 normal actions per turn questing or other story actions. And, I would be in favor in questing to the Forbidden Forest next turn if we get Protego (Deep Understanding).
But, character and story wise, upping Charms/Transfigurations/DADA is both well within character (he is a bit of a Newt Scamander in his focus) and optimal for growth. Focusing on these subject is not curtailing Jacob's life but actually will help him and the story. First, there is the immediate goal of winning the Dueling competition, but there are also the goals of researching the spells/potions needed for him to pass his classes and to go on adventures, and when he is on adventures the most common actions he does is...Charms, Transfigurations, and DADA. It isn't just enough to be able to go to the adventure, after all, but to excel at them.
I agree that Jacob also has reason to study Occulmancy and Understanding Magical Creatures. But, I'd argue that Jacob has a greater interest in the three topics. Though I'd agree that Occulmancy is something he might probably formed an interest in- but not obsessively so given him not even trying to trick Dumbledore in the most recent post (yes, we failed the check, but in-story Jacob was fine opening up to Dumbledore).
If we want to have more adventures over the year (versus beelining to one specific adventure or two), it is better to get the key skills that Jacob already is obsessed with up to A+ this year. Then use any Personal Actions saved by the better bonus to prep for all future adventures. Not saying the Occulmancy isn't something that we should do.
My point is that there is a current short-term goal that is available and doable within the next few months that has long-term benefits (getting Charms, Transfigurations, and DADA up) and that we shouldn't ignore it in favor of working on what could be a short/medium-term goal (adventuring to the sea). And, with the short-term goal done, the results of our adventures might actually improve.
There is a reason people aren't doing that. Pouring 4 actions into one subject during one turn is essentially pushing over a years worth of study into a single month. Jacob is a prodigy no doubt, but I'm fairly certain that would prompt a sanity check of some sort.
I won't speculate as to what the QM would do. But, we don't need to put 4 subjects into 1 turn. If we start next turn, we could do 2 actions for 2 subjects per turn and 1 action for DADA for 1 turn. With the +20 to training rolls, the DC for DADA, Charms, and Transfiguration is DC 5 so there is a pretty good probability of succeeding.
As for the spells, my plan does have Protego and one of the mandatory potions as the main priorities so, though I did leave the other one a little further down the list tbf.
Well, I think the issue is the amount of actions you're putting in and the DC of the research and the order. Protego (Deep Understanding) is DC 150.
With DADA +9, Intellect +7, Creativity +5, the bonus is +21. With an average roll of 50, that is an average +71 per action. Which means there is a pretty good chance it would take all 3 actions to get it. (Note that with a DADA of E-, it would be a +27, which would be an average of +77 and a pretty good chance it would only take 2 actions to get and thus saving us 1 personal action).
The remaining Potions are a DC 28 and DC 100. And the DC 100 is the fourth on the list. So, if we roll well, we would still have a DC 100 potion research remaining. Even if we rolled improbably well. And with less time, we may overcommit to get the DC 100 potion done in time.