I think technically if the stroller is functioning as a wheelchair, they must allow it all the places a wheelchair is allowed. Similarly, they may ask people to transfer from their wheelchair for convenience sake because tables ARE close together, but they cannot make me leave my wheelchair elsewhere.
That does not mean, however, every CM will be versed in ADA law, which admitted is very fuzzy when it comes to using non "official" mobility devices.
The GAC does not work in restaurants, or really anything other than attractions.
I would suggest for any table service reservations, which you would need for character meals anyway, when you make the ADRs, let them know that you have an auitistic child who requires his stroller-as-wheelchair in the restaurant. Tell the reservationist that you either need a booth (where it is easier to create safe place no one can escape from, and that you would prefer instead to be allowed to bring the stroller in. They will just try to give you a table where the stroller/wheelchair can it.
The person on the phone puts a note in the system, which the restaurant looks at as they are planning their meal. Whenever possible I stop by the restaurant earlier that day and tell them I have a reservation and that I need to bring my wheelchair inside with me. This just gives then a few hours heads up.
SInce you have a stroller and not a wheelchair, I am not sure if this would work for you, but i just wanted to tell you what works for me.