If this is a slightly more commercial kindergarten, I think the issue with your back can be easily solved. However, I believe the sisters and teachers would prefer to spend the money for the children, not for the parents. I believe you and the other parents wouldn't mind to be slightly uncomfortable.
September and October children are the toughest cases, since they would be consider "too big" sometimes as super big B and small being small B.
But no need to give up, there are still many choices and the most important thing is a caring family. There are certainly some kindergartens which will at least allow her application. Alternatively, you can try to apply K2. Good luck!