How to convert from one type of relationship table to another type
You can add columns to the existing tables.  These should be initially nullable until the data is loaded.  After that you can alter the column definition to NOT NULL if appropriate.  You can also drop columns from the table definition.

The process I use is:


Add new columns to table definition.
Populate new columns. (Before using code that expects these columns to be populated.)
Alter old NOT NULL columns to NULL. (Before using code that doesn't populate these columns.)
Make new columns NOT NULL where appropriate. (After code that doesn't populate these columns has been retired. May require rerun of population scripts.)
Drop old columns.  (Can be done much later.)


These steps may be done over a period of days or weeks.  This depends on your development process.  The population script should be able to identify and populate rows created or modified by old code.