Off the top of my head we could research, magically:
1. How to 'transfer' grief from one puella to another
2. How to numb emotions, or put someone in a protective 'emotion coma'
2.5 This could probably help protect against telepathic intrusions, actually.
3. How to replicate Kaoru's song through magitech
4. etc. etc. etc.
Those are some cool ideas...
To take a relatively benign example, exposure therapy is really easy in theory. Someone who is scared of spiders should try and walk into a spiderweb whenever they see one. They see it, they walk into it, and slowly they will get over their fear of spiders. That's sort of how you train astronauts to do well under pressure, and ditto with surgeons. You bombard them with every conceivable scenario and they slowly become these people who can do amazing things no matter what the situation because they're used to pressure, instead of us mere mortals who tend to fumble around and do somewhat worse.
If you suggest to someone who is phobic of spiders to do this a bunch of them will start will crawling up the walls to get away from your crazy-ass notion no matter how reliable it has proven to be. Depressed people probably won't (grief spirals are pretty reminiscent of depression), but they won't be ecstatic either that you've decided to number crunch something that's very personal to them and top it off by saying 'well, this would be easy to solve, a sixteen year old girl could manage it after reading things up on the internet for a few months'.
Not to mention, how would you make someone risk adverse to grief spirals? Sounds like something very risky to experiment on - risk of death risky.
It's one of the Meguca's jobs to be the dorm's "Secret Fairy Godmother" and they go around doing nice things all month. The floors someone complained about are suddenly sparkling clean, the toilet paper has been restocked on time, there are pancakes for breakfast, and the dishes have been washed. Someone who's having trouble with their homework gets a little note directing them to a helpful website, someone else having trouble in general gets a note directing them to a tutoring service. Someone with money trouble gets a little extra, and someone with trouble fitting in finds themselves surrounded by friends.
And you can send messages to that Secret Fairy Godmother. Like: 'thank you!' or 'I think Ohta is having boy troubles,' or 'the new girls r griefing, plz help', and so on, and maybe that Secret Fairy Godmother will give you tasks every now and then, and if she's helped you before you will feel well disposed to help her back.
That's a cool idea. Although that would probably fall under the morale boosting mechanic it really is a good idea.