The only time my daughter was picked was when we walked in two minutes before the show and got to sit in the front row, usually reserved for guests with
ECVs and their family (also I think VIP guests get to sit there).
We have been there once with a fastpass (literally the first ones in the theater) and have gotten there super early other times but due to the fact that the best seats are always reserved for those with disabilities until the last couple of minutes and there are not front row seats available for anyone else, it is very difficult to have your child chosen to participate if you are not a VIP or with someone deemed to have a disability.
I can often figure out what to do to have a certain experience at Disney, but the only thing I have been able to do with this show is to wait until the last minute and hope that they let us sit in the first couple of rows.