Especially with moving often, it might be worth it to pay for an advocate to help you negotiate the new IEP each time you move.
We had PT denied in MN, as not educational. Moved to OH, boom, fully covered because in little kids, PT helps socially (can't keep up with other kids on playground) and core strength carries to arms for fine motor which is definitely educational. Now no matter where else we move we will fight for PT to be covered under those grounds.
It kind of depends on the specific therapy if you want more advice than that. Feel free to PM me.
I have one special needs kid. He does not have an ASD diagnosis, but it his profile dead on. We have not had any trouble getting the services he needs without the ASD diagnosis, although we would have to doctor hop to get it if we ever wanted to ask the public school to pay for private school, which in OH you can do.
Adults with ASD have very high unemployment rates. It may effect our ability to retire early. We may end up supporting our son for much longer than age 18, either financially or emotionally/behaviorally. At this point, at age 8, ER is planned for around ten years out. So much can change in that amount of time that we aren't worried about calculating an exact date and mapping out all contingencies.