Hi David,
you can copy the table with a "insert into tblcopyfact select <all the fields> from tblfact<Model>"
add your dimension with at least one record inside, full process
and replace the data with a reverse "insert into" adding in the right place of the field list, the default value for the new dimension and full reprocess the dim and after the modify model with process application to rebuild the OLAP.
Regards
Roberto