Ahh the Omiyage Lie. I love every minute of it. A unique thing for JETs exclusively, as no one else brings "Hi, I'm new here and I brought you all X country stuff".
I swear it must've started by a bunch of overly genki ALTs 20 years ago and the tradition continues. Don't bother, it's not expected, and isn't gonna do anything for ya. Heck, when Japanese people go on Vacation they barely bring back enough omiyage for their department, let alone the school, and noone cares. That being said, do bring a thank you gift for your supervisor (and homestay if you have one of these for a few days) as these people will be going out of their way for you for the first little bit and a polite thank you is a good thing.
I'm actually pretty happy with the list, but I will mention a few things:
3 prong adapters are not required. Grab a pair of pliers and break off the round grounding plug. Problem solved.
bug related stuff. You can get it here.
sunscreen? Because Japan doesn't have sun... ever. It just doesn't happen in the land of the rising SUN.
External Hard drive (Full o Stuff only, no point in bringing an empty one)
Thermal gear. POINTLESS. The thermal gear here in Japan is fantastic, cheap, and readily available. Buy it when you decide you need it.
Chocolate chips? Seriously? www.amazon.co.jp/www.rakuten.jp
and the problem is solved.]
Your list for "omiyage" isn't omiyage, it's classroom materials.
To add to the list:
Do not bring your ps3 console, do bring your ps3 games. You can buy cheap used ps3's here for very little.
Do bring your Xbox/wii if you need to play english games, but know they won't play j-games.
Do bring your blu-rays if you own them, but only if you really care about quality (you won't have a big TV here... unless you buy it yourself)
Stuffed Animals. Personal things. Knickknacks. Look around your room and find those things you've grown up with and bring them along. You just might need them one day.
Do not bring your desktop/monitor here. If you're comfortable with it, bring your parts, leave your case behind and buy a new one in country.
If you are going to be biking/walking a lot and will be bringing a computer with you to work (some ALTs do this) consider buying a light laptop that isn't very powerful for work (ie disposable in case crap happens), and a good/powerful one for home.