I have no idea why anything other than N2 and N1 exist. N3 is basically useless, I got it in under 6 months of studying and I’m a slow learner (my Korean and Chinese peers were going for N2 at that time). I still couldn’t function well with it. I was so disappointed by it I skipped 2 and went straight to N1.

The company I work for has offices in the U.S. and Japan. They were able to transfer me to Japan and let me work remote with my team in the U.S. They probably would have been able to get me a work visa, too, though it wasn't necessary in my case since the spousal visa was much simpler to obtain. Since my company has a presence in Japan, all of typical payroll, benefits, insurance stuff is handled through the Japan HR dept.

For anyone looking to spend time living abroad, I think this approach of working for a large multinational and asking to be transferred is a viable option. Of course it requires that you have a tremendous level of trust with your manager, and you need to be senior enough that it is worth the hassle for them. Also - if there is no business justification for the transfer, don't expect them to help out with relocation costs, and if you are moving to an area with a lower cost of living they may give you a negative cost of living adjustment, too.

I should make it clear that this move wasn't easy to make by any means. It took years of planning and even a job change to find a team I was confident enough I could make it worth with. While getting the visa was simple enough in my case, actually moving to Japan and buying a house, opening up bank accounts, getting a drivers license, etc were all enormously time consuming and at times very frustrating.

So it can be done, and I feel it is worth it, but it does require a fairly large amount of effort.