Custom pocket door with insulation, water pipes and tile!
3/16" is an awfully fine clearance for a pocket door.  Unless the door is moisture-proof, the door is going to bow (and therefore jam when moved) whenever there is a humidity difference across it such as when there is a shower in use.

That is a completely unacceptable place to run plumbing.  Heck, getting 3/4 inch galvanized pipe crossing each other inside a 2x4 wall is a challenge and not something a mechanical inspector wants to see unless the circumstances are truly difficult.