IMHO you are going through alot of trouble but then I'm reminded of
something my Dad use to tell me...."If you over build it you won't have to
worry about it"
I assume you are trying to avoid visible signs of fasteners. How about
using panel adhesive? You could trowel it on to get an even spread, nail
around the perimeter where the crown would cover and use a separate piece of
ply tacked in place again where it will be covered and use some jacks to
apply pressure till the glue sets. Jacks being pieces of wood just a hair
longer than needed and flexible enough to wedge in place.