I believe that the general wording of the law is that the school is only required to pay for those services that are required and in the IEP, and if those services can not be provided by the district, and you may have to go through some effort to prove they are not, then the district must pay for it. This includes therapies and evaluations. It includes MFEs if you can provide evidence that the school is not able to perform a fair and adequate MFE on your child (or in my case, we had a therapist that had just done a full diagnostic battery on Brandon two months before he turned 3...those tests were then assigned as the results to his MFE so the district did not have to do anything).
Also check out your state laws. Here in Ohio, it is much easier to provide evidence that FAPE can't always be provided by the district for a child with an ASD. We have the Ohio Autism Scholarship Program here, and we have had absolutely no problem with the district agreeing to let us leave the district for our own private services (which are indirectly paid for by the district...the DOE takes the money from the district, up to $20,000 a year, and pays the providers with it).
But in general, you're not going to get the school to willingly pay for private services, and especially not for homeschooling (since the district typically doesn't even get money for homeschooling children), unless you can provide evidence that the district can't meet the FAPE needs they are legally required to meet. This is often the case in rural or poor districts who may not have appropriate service providers on staff. It also may be the case if your child is absolutely not able to learn in the typical classroom environment. But I think that if your district *can* provide appropriate education for your child, you will have an extremely uphill battle in getting them to pay for more expensive private services.
In general, I'd recommend checking with your state laws--especially if you have school choice or charter school laws, as well as disability programs/waivers provided by the DOE. Those will help determine how easy the fight will be.