I am in a similar predicament and initially was intending to blow in fiberglass. After enough research I decided against this and have been dismantling the flat roof. In my case most of the roofing was gone so all I need to do is remove the 1 by decking. Sounds like this will be impractical for you. In your shoes I might consider loose polystyrene balls blown in.
"Ask me anything. If I don't know the answer I'll make something up."