Good news everyone!
I just found a report that says that from next year public servants (I presume this includes us teaching types) and homemakers will also be able to open J401k accounts, provided they are paying into the national pension scheme.
I found partial confirmation here (click through to 公務員) and this blog post claims the expanded eligibility will start in January 2017.
If true, this is very good news indeed. I will let you know if I find confirmation of this and of course if I manage to open an account :D