Approaches for Real time copy of database on same SQL Server instance
Transactional replication gets you close, but as you said, changing the subscriber schema is a recipe for disaster.

Transactional replication uses stored procedures to apply the data changes. You could, with every table change, change those procedures to deal with the underlying changes. 
That is a lot of additional manual work, but I don't think you will find a solution without that. Those procedures are created automatically when calling sp_addarticle (See value 0x02 for the @schema_option parameter and the @ins_cmd, @upd_cmd and @del_cmd parameters.)

However, you might be better of to take a copy at the beginning of the development cycle and then not apply new changes till the end of the cycle. That is a simple backup-restore with the added benefit that you do not have to constantly adjust testing scripts do deal with the changing data.