MooseX::Storage is no more magic then Moose is, if you want your MooseX::Storage enabled object to be turned into a HASH ref, you just need to call the pack method on it. And to restore it from a HASH ref you call the unpack method.

As for using it with HTTP::Session, you likely just want to wrap HTTP::Session and either override the get/set methods to watch for any MooseX::Storage enabled objects, or have a special {get,set}_moose_object method that handles things for you.