how to replicate articles from different schemas?
The meta-answer to this is to use SSMS to publish the article and examine the replication scripts.  The answer is that the @source_owner parameter to sp_addarticle has the target schema.  This dates from before schema/owner separation in SQL 2005, where an object owner and a schema were the same thing.

And the script you list uses does not publish dbo.Product, it publishes Production.Product