Organic meat and etc in the Tokyo area?

I'm on a strict diet in which I basically cannot eat more than 20 or so grams of carbs a day without getting very ill, so I mostly stick to animal products. I'd like to visit Japan some time this winter, but upon contacting the Japanese embassy it has come to my attention that I won't be allowed to take any edible animal products from my country (USA) into Japan with me to tide me over (which in my not-so-humble opinion makes absolutely no sense if they're proven to be safe for consumption), which means I'll need to be able to get food immediately. Due to both moral and health reasons, I only consume organic free range animal products.

I've been looking for a while now, but I can't seem to find any reliable sources, and I'm beginning to worry that I may not be able to go. I need to find somewhere where I can buy things like eggs, cheeses, and various meat products. There's also the concern of radiation lately, so I'm beginning to wonder if I shouldn't just import my meat from one of the allowed countries? I'd like to avoid that if possible though, since it'll be fairly expensive considering that I consume a few thousand calories daily.

So long story short, does anybody know where I can get reliable organic free range safe-for-consumption animal products in Japan? Bonus points if you know of any restaurants that serve such fare in the Tokyo area~

Any advice would be immensely and (probably) eternally appreciated :)

Most shizen-shoku-ten (natural food stores, not to be confused with kenko-shokuhin-ten that can be transated as health food stores) carry that kind of meat.

In Tokyo area, F&F and Kodawariya are among the trusted ones.
http://www.shizensyoku-ff.com/
http://www.kodawariichiba.com/

If you know which area you're staying in, perhaps someone may be able to assist you on finding branches or other reliable stores nearby.

If you're going to live here, you can become a member of natural food delivery service groups such as Daichi
http://www.daichi.or.jp/

They have there own policies on radiation levels and set their standards harsher than the government's. While supporting farmers from eastern Japan by keep selling their products only by their harsh standards, they also handle "products from western Japan" for those who may feel better that way.

The following are cafes and restaurants that mainly serve Daichi products.
http://www.daichi-keats.jp/
http://www.yamafuji.net/
http://tabelog.com/tokyo/A1317/A131715/13079565/

I'm sure other stores have their own standards as well. Check them out.

Bon Appetit!