Good travel insurance options while setting up NHI?

I just learned that I can't use our Airbnb to register with NHI. We'll be in the Airbnb for 6 weeks while we look for longer-term housing in Fukuoka. I heard American Express has good travel insurance but they don't serve my state, which totally sucks because I trust them and that would've made this easy.

I should have international health coverage from my job for about one month into our stay, but that last few weeks in the Airbnb, I am trying to cover in case we haven't found our new place yet. Thanks for any recommendations.