Do you have any recommendations for voluntary car insurance on a vehicle I lease and don’t own?

I am living in the inaka and plan to stay until August next year. I am leasing a vehicle from a local dealer because that was the most convenient option when I got here, but recently they restructured the deal. They stopped covering my voluntary insurance, but then offered me a plan with their affiliate for ¥15,000 a month (ouch). I want to find it elsewhere, but the companies I’ve looked into thus far don’t want to insure me if I don’t own the car. When I try to research insurance for leased cars I get a lot of results for travel rentals, and that’s not what I’m going for, so I’m hoping to find advice here.

Has anyone else been in a similar situation? Can you recommend any insurance companies that have a reasonable price?

For what it’s worth, I just received my Japanese driver’s license. It’s a green license exempt from beginner stickers.

Thank you in advance!