I'm not sure if Service Broker is the appropriate tool to "copy" that much databases. Maybe you should think about replication, in your case it might be transactional replication.
The only thing to bear in mind: replication does not transfer statements transactional. But maybe you did not care of this in your Service Broker procedures, you can check that.
If transactional consistency is not a big matter on your destination databases think of using replication.