The neuropsychologist that just tested my daughter said the district is using a very strict definition of the law.
A lawyer thinks we could win a lawsuit to get the district to pay for the private school. We are going to do some more research about that.
I live in Texas, so what I'm saying may not apply to your situation at all. One of the things that teachers have to do here in Texas is "differentiate" the material to be learned according to the needs of the students. If your daughter were here, her teacher would be expected to incorporate into her regular education reading, at least to some extent, the multi-sensory approach that you mentioned, since that is a way that she can learn. I teach high school Spanish at the middle school level, and my teaching set includes multisensory learning activities for students who will benefit from them. It's not that complicated, and the resources are out there.