Well if you have had the experience before, it means that you do have experience and you also have a portfolio of pictures? If you still have good relations with your agency you can always contact them again to find about about agencys in Japan (they might not be able to help but never know until you ask).

If you do work as a model the visa will fall under "Entertainer" and the visa durations range from:
- 15 days
- 3 months
- 6 months
- 1 year

The duration of your visa id imagine out of the above depends on the contract you will be working with. Once this Visa expires you need to either renew it (and get a new working contract) or you will have to leave.

When i mean long term i meant many years, how long do you think you would like to spend in Japan? If you get enough contracts to keep renewing it could be possible for as long as you keep getting work. But id say applying for Permanent Residency will be very tough.