Austin Auger here, and I actually had a question for you as I am a bit perplexed at the moment. I am mixed Japanese, and am trying to get to do some work in the Japanese market. Are there any specific agencies that you might be able to think of out here in LA that I could possible look into who has specific relationships with Japan? I have been looking into a lot of agencies on the Japanese end, but you must be living there already, and they really aren't into visa sponsoring of newer faces.
Let's work backwards through your questions. Yes, you are correct, agencies don't support visa sponsoring for models. Agent's don't technically hire you, you hire them. So they can't sponsor you. What they will do is help you file the paperwork to work in another country. I would suggest asking your agents to file the paper work for you. They do this often and the process is simple for them. Perhaps have them get a letter from agent relationships in Japan to show that you are going to be traveling for work through that agency.
There are quite a few men's modeling and commercial agencies in Los Angeles. Check out Abrams, Next and Ford. All are very good and reputable. All have relationships with Japan.
Lastly, don't waste time being perplexed. Everyone in the industry is. It all changes so fast. Tomorrow's a new day and hopefully for you... a new visa!
xxEmily ~ SupermodelBlogger