A router (for WOOD WORKING not internet) with the proper bit, set to the proper depth would be my first choice. Even a cheapo router and bits from Harbor Freight shouldn't set you back much at all.
Your suggestion could work but would sacrifice some strength and depend on having a good glue bond..
Plywood is made using alternating layers of wood plus specific glues for the laminating process and is put under many tons per square inch of pressure while the glue sets.. You will never be able to match that using your idea.