What to do about annual heath check if local hospital is completely booked

I live in the middle of nowhere in the Japanese countryside and there’s only one hospital available. I went to book an appointment for my company medical check and the hospital is booked until January 2027. Has anyone ever had this happen before? If so, what did you do? Does the company pay for you to travel or give you time off to take it further away? Thank you in advance for your help!

by 7Yuki-Chan7