Control SQL Server pace of db shrink to split into multiple files
You don't need to shrink to migrate data to multiple files.
Simply add the new files tot the filegroup, then rebuild each table one-by-one to move the data around.
The proportional fill algorithm will take care of equally balancing the data between the files, assuming you size the files in an optimal way.  See this Microsoft Docs page for details.
Use the ALTER TABLE ... REBUILD; command to migrate the data across all available files in a filegroup.  You can even use that command to migrate a table to another filegroup.  Microsoft Docs for that command are here