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Well, I definitely recommend getting more face-time with Japanese conversation while you can during the summer. Especially if you choose to live in a dorm (I lived the the Nagoya Koryuu Kaikan [also where I found my significant other but that's a different story]). Getting acquainted early with the fucked up language that Japanese college students call "Japanese" will make your life outside of school much more comfortable. No one really speaks Nagoyaben (except old people you'll meet on the street) but its definitely in some areas of youth language (しとる instead of している, わ instead of よ). You might not pick up all of it in 4 months but you'll start to recognize it. I'd just recommend getting some speaking practice in now, even if its by yourself. You can read and write kanji anywhere in the world.
Knowing more kanji is good but there's grammar and writing that also factor into the test. It at least sounds like you know what you're doing, so don't worry about it; you'll do fine. Again, I'd stress going over what you already know. There's homework and whatnot but you'll have plenty of time to go out and experience stuff. I only studied (books, desk, denshi jisho) when I had to and I feel like I got a better experience because of it.
Well, depending on how you're going to Nanzan (exchange, IES, scholarship program etc.) you'll probably get different things at different times but I went through Indiana University and got packets with prep-material to get my visa, course expectations, schedules, dorm info, everything. I have it (the kanji/grammar list) handy but I don't really have a way to scan it or anything. You'll probably be getting it at some point soon. Also when/if you get the brochure, I wrote an article on the Japanese Literature IV elective they offer. Just sayin'.
Hamada's very prescriptive but just a really good educator. Tsuda is the sweetest little old Japanese lady ever and will do EVERYTHING to make sure you understand the lesson. I also had a bro named Hanashiro who bounced back between 600 and 400/500. I describe him as a creepy uncle. He's hard into gunpla and cracks little jokes to himself. I liked him but I didn't learn that much in his class. I had a roommate who had Okada and she was described as the hardest bitch ever. People would be confused and ask her to go over something again and she would outright ignore or even laugh at them. She was just a hardass. I'd also recommend any elective classes from Yamada (sweet, genius lady), Hosoya (eccentric, thinks he knows English Japanese literature professor and Todai grad), or Matsuda (another sweet old(er) lady who lived in Wisconsin and is pretty good at English). I liked 'em. Maybe you will.
There was a lot of in-class writing in IJ600. Pretty much every day. I never really practiced writing before but it wouldn't hurt to go over a few. It's actually easier in some ways to just write hiragana for a word you're not sure about (they'll take of points if the kanji is wrong or illegible but they wont if its in hiragana). Basically, if you want to practice, you can. But it won't make a huge difference. You'll learn what you need to for kanji tests and that's about it.