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[x] Surein Toroi's Book Shop - We got ofuda book from there, something that helped us immensely.

[x] Blood Red Stone
The servant I'm guessing for this sounds the most interesting of all of them.

We roped her into mentoring Rin after our supposed death.

I don't think that Einzberns subscribe to wizarding newspapers.

Clearing Room of Hidden Things can probably be done later. Even if he will be cut out from Hogwarts, manor should stay safe and so the link.
Visiting British Museum can create good connections, but...

He needs to become franchise. It's time for Shinji Incorporated!

I really need to check this thread more often, I've missed so many questions.

Start? Isn't this like almost his whole life? He is basically magical Batman in making. Also, with the amount of the...

[x] Exploring the grounds together

It's still not something new like you initially suggested, which is my point (also three years of competent DADA teachers).

You remember that he was tutored by Tomas as a form of practicing occlumency?

Sparring sounds nice, but two of those champion's will be your enemies. And considering that Shinji is not powerhouse here, he may lose more by showing his tricks than gain by learning those of other...

Broken chains are now longer that the first HP book, and the school year is yet to begin. Goblet of Fire was 2.5 times longer than Philosopher's Stone, I suspect that with much more happening this...

Defensive fighting doesn't seem to be the best way to win Hokuto respect and will probably make us lose easily. On the other hand it may be beneficial to not reveal all our tricks to her.
Hokuto:...

[x] Getting to know the Raven Commander

[x] Visit the Room of Requirement and consult with the ghosts of Hogwarts on what's going on
I still think that Hogwarts is important, and we should at least follow situation here.

[x] Fred
[x]...

[x] Refers George to Tomas, as the puppet is a master duelist
Outside of fighting, he may temper some of bad tendencies that George is developing.

[x] Tomas, who is good at countering various...

[x] Draco Malfoy
I hope for some insights into what his dad is doing.

[x] Harry

[ ] Talk to Lockhart - with the way the man speaks, he has likely seen war, and might better know how to talk to someone in Harry's position
All the other options seems to be harmful. Either Harry...

[x] ...that an open call for a coordinator be put out, with applicants tested for leadership abilities through mock scenarios
[x] Hogwarts

I have a feeling that things are set up for internal...

Because "You're forcing your own games in my sandbox, you damn half-goblin!". Of course said dofferently.

It resizes.
Edit: Ninja'd

How is going to Flitwick supposed to help support better integration between students from different school? You get Hogwarts's headmaster to help organise Hogwarts students' idea. And it's not even...

He gets one in fusion form.

We are trying to promote cooperation, so let's cooperate.
[x] (Write-in by Skull Leader) Get all the schools involved by talking with all three schools champions, and the three banner leaders in...

As others already said, Shinji's road so far was inseparably connected with knowledge, and it paid off so far, thus it only makes sense to continue following it.
And I believe that Shinji is skilled...