I've not really had a problem with Japanese software, but I mostly stick to old games and the like. You do need to make sure you install cjk fonts, and if your system locale isn't Japanese you need to make sure jp locale is enabled then set it before running with `LANG="ja_JP.UTF8"` (or possibly LC_ALL if that fails) but other than that I've not had any major problems.
I've used all the Japanese language and font settings (including your suggestions), and I have fonts installed, and for what barely runs this gets the fonts mostly working. It makes no difference for what doesn't even install. One example is 3D My Home Designer PRO (version 8 which is not the latest, but one I have a license for. From Megasoft, Japan). It's exclusively for Windows.
Another example (which is not licensed, and easier to test for) is Jw_cad https://www.jwcad.net/download.htm which actually installs and runs, it's just that it doesn't run well. Some stuff works, but it's not enough to make it usable.
What kind of software isn't working?