I read through the chapter today and enjoyed it overall. It's not perfect and I do have some criticisms, but in terms of writing I definitely think it's an improvement. The change from Kyon's narrative to 3rd person seems to be working out well for you. Anyway, I want to do a thorough job with my feedback so I'm afraid I'm going to put off the full response for another day or two (apologies!), but this looks like a good start.
So...finally, here's the much delayed feedback. Apologies for the wait, but I'm something of a procrastinator and I was busy this past week. Anyway, the first scene is fairly good and Galus's part in it was a pleasant surprise. I honestly wasn't expecting him to show up again anytime soon, and it's nice to see him in a different role than ranting comic book villain. His conversation with Nanoha was interesting, and while I think his mental leap connecting SOS propaganda to ethnic cleansing is a bit of a stretch his efforts to (apparently successfully) plant doubts in Nanoha's mind seem quite in character for him.
The physical description of his cell was clear too, and I got the sense that you were channeling Magneto's imprisonment from the X-men movies.
I already commented on the Jinnai, Haruhi, and Nanami scene earlier, and I think you incorporated it into this chapter well.
The next scene with Kyon and Nanoha was cute and it's good to know that Kyon is still as perceptive as ever. With minds as devious and unpredictable as Haruhi and Jinnai, that's a talent he might need soon. Without Kyon's narrative, though, you're going to have to find other ways to present his characteristic sarcasm.
I'm a bit ambivalent about the class idea. It sounds like a good way to get the main characters together regularly, but with their different interests, activities, and schedules I'm not sure how much sense this makes. Is Haruhi supposed to shuttle back and forth from the Hive to Florestica 6 days a week, take classes, and learn how to run an empire while simultaneously actually running the empire? Or how about Nanami's business ventures and Makoto's scientific pursuits? And is putting Jinnai and Makoto in the same room on a nearly daily basis such a good idea? A once per week class or something to that effect might work better.
The scene with Makoto and Yuki was unexpected but also intriguing on some levels with the hints of a developing romance. Heh, sometimes I wonder if the trip to El-Hazard gave the "Wanderers" two powers each instead of one: almost instant recovery from any injury on Jinnai's part, the ability to arrive in the nick of time to save someone for Fujisawa, Nanami's power to put together a restaurant and cook Japanese food no matter where she is, and Makoto's harem-generation power. More seriously, his love for Ifurita is so strong that I have a hard time picturing him falling for anyone else except in a moment of utter despair, but that same devotion seems to make him blind to the effects his pure heart, brilliant mind, and genuine willingness to help others have on others. Yuki doesn't come across as the type to act on any romantic feelings she might develop, though, so if you're trying to spark something between them then you face the hurdles of a character who is unambiguously in love with someone else and another character who seems content not to act on such feelings.
Anyway, I think you went a bit overboard with the scene description here. I mean, petri dishes of Demon God DNA samples and textbooks on Quantum Mechanics? Considering the technology level of El-Hazard's contemporary humans, books on quantum mechanics and genetic research seem more than a bit advanced and out of place. Remember, Dr. Schtalubaugh is not Dr. Light and while relics from the past lying around Makoto's room make sense a full-blown state of the art futuristic lab does not. :)
As for the scene with Jinnai and Diva, I kind of like what you seem to be developing here but I'm not sure how it would realistically be executed. Jinnai revels in conquest and the elation of victory so I can understand why he'd be so eager to wage another war, but how exactly would one invade Phantom Tribe territory when their entire society seems to be hidden and they probably have secret enclaves throughout Alliance lands?
Considering how they operate and how hated they are, I kind of doubt the Phantom Tribe has a chunk of land they publicly call their own that the rest of the world knows about. And I'm disinclined to believe that Haruhi would condone the subjugation of an entire race, though after what Galus did to her I can understand her developing a dislike and distrust of the Phantom Tribe in general. At the very least, though, the set-up is ripe for Nanoha (and possibly Galus too if matters progress in such a manner as to convince Nanoha that she should free him) to play a significant role.Regardless, thanks for sharing and apologies if this sounds a bit rushed. I went out to dinner with my brother and his girlfriend after work today so I was busier than I expected.