should I do DE for nursing?

As far as I know, there are no pre-licensure distance programs that you would be able to do in Japan. There are some bridge programs such as LPN-BSN or LPN-RN, but they require some kind of licensure or certification to enroll. And yes, it does matter to some states where you get your RN because state boards of nursing will always look at the source of your RN. If they don't recognize your program, you don't get a license.

Even if you didn't do an accelerated BSN program but went to a traditional BSN program, it wouldn't be a matter of "4 more years," because many of the general ed credits you already have from your existing BA would transfer in -- you wouldn't have to start over from scratch.

Accelerated BSN programs are just all the purely nursing content of a traditional BSN program shoehorned into a shorter amount of time. They are very rigorous and demanding because of that, because of the increased pace of the program. Most traditional BSN programs are set up as two years of general ed/prerequisites and two years of the nursing courses. Plenty of traditional programs accept people into just the two years of the actual nursing courses (in fact, in many schools, including the last BSN program in which I taught, student were "pre-nursing" majors for the first two years, and that was no guarantee that they would be accepted into the nursing program for the last two years -- everyone applied separately to the nursing program toward the end of their sophomore year). You could talk to the schools near you, or that you are interested in, and see what they have to offer you (and I would encourage you to do so -- and talk to all the schools you think might be possibilities for you). In my experience, schools are glad to look at and talk to you about unofficial transcripts (which many schools will give you for free), although you would eventually need official transcripts to actually apply to a program.