Leaving quickly due to health problems: What to do about final bills?

I currently live in Japan!

I need to leave Japan due to health issues that I would rather be close to family to deal with. I am looking at a window of 2-3 weeks.

I know that my utilities providers will want someone to send the final bills to after I've left. I'm going down my list of (responsible) friends, but so far, everyone has refused, even though I am fully prepared to leave them with more than enough cash to pay everything. Japanese friends are reluctant to share their address (predictable), and it seems all my foreign friends have been burned before helping other foreigners in the past.

I do plan on coming back to Japan once my health gets better, and I don't want to add to the list of foreigners who just walk out on payments making things harder for everyone else.

What options do I have in the event that I can't find anyone willing to help?