Re changing districts vs out of district placement -
We started K in an interdistrict magnet in a neighboring large city. They refused to do anything for DD despite our outside OT eval showing significant fine motor deficits. Wouldn't evaluate for in school services saying "she'd never qualify - she's too smart." K teacher actively punished DD for her disabilities saying "if she doesn't have an IEP or 504 and doesn't complete the writing assignment she doesn't go to recess. Period." Nevermind that she was in OT learning how to hold a pencil and was not physically able to complete the writing assignment. If we were residents of that district there would have been NOTHING we could do to get appropriate services for DD. Even going to due process would not have netted much benefit. We would have had to move, send her to private or continue as best we could with outside resources.
Fortunately our home district intervened with testing. We happen to live in a district with excellent spec Ed services so transferred to our neighborhood public for 1st grade. It's a large district with a lot of resources. And they *never* go to due process. So if you do your homework, line your ducks in a row and refuse to blink your child gets what they need. It is easier if you have some kind of a round peg to fit into a protocol of some type, harder if your kid is outside the box like mine. We had an absolutely awful principal who viewed the kids as little data points and whose MO was to make life miserable for any little "outlier" until they were removed from her school. Selling your house, homeschooling, sending to private - all were fine because your kid was no longer her problem. We stared her down, reported her behavior to the department of education and held the district responsible and finally got out of district placement at their expense. (And the principal was simultaneously removed for a position at central office analyzing data for the district...)
When things were at their worst we considered changing districts. Rather than buying and selling we were going to rent out our house and rent in a better district. We were advised not to because in our case we were so close to winning out of district placement. However the lesson I learned is to look closely at the history of any potential district before you transfer. Some districts will fight at any cost to prevent OOD because they don't want to establish a precedent for others to follow. They use intimidation and you may have to be prepared to spend $30k-$50k in the process. Most families will choose to move, homeschool or pay for private instead.
An experienced advocate intimately familiar with your local options is probably your best bet.