However, if you wanted to take a 1 year sabbatical, you could get a job as an engineer with a Japanese company, work for a year, apply for fast track permanent residency at the end of that year (you’ll need to meet some education/income requirements), then go back to your old job remotely. There are software jobs that hire people who don’t speak Japanese.
NO.
You must have a work visa to live here, and you won't get that unless a Japanese company sponsors your visa. A US company can't do that for obvious reasons, unless it's a company with a Japanese branch office.
The only way to do what you ask is to get permanent residence first, but that means living here for a while on a work visa or spouse visa.
Also, on top of this, the US company may have issues with you living outside the US while working for them, but that'll be the case for any other country. This was discussed within the last week or so here on HN.
I also pretty much exclusively have software experience in government contracting so the jump to commercial would be pretty big too.
Or you can work at an American company like Google (not sure if they're still hiring though; I thought I read they had a company-wide hiring freeze).
I am not trying to discourage you, but if you really want to live in Japan, you have to learn Japanese, which is not an easy language to learn, especially for English speakers, even if you live in Tokyo.
edit: wording