Now, this answer is based on my knowledge of EF4.3, so I hope the migrations work roughly the same in EF5 :) After you've created a migration, you should be able to add code in the Up and Down methods, between the dropping of the old property and the creation of the new property. This code should move the property data in the correct direction. I've solved it with the SQL() method in where you can enter raw SQL to perform the data move.
In the Up method of the migration:
SQL("update [TheTable] set [NewColumn] = [OldColumn]");
and in the Down() method:
SQL("update [TheTable] set [OldColumn] = [NewColumn]");
The disadvantage of this approach is that you might couple your code with the database you're working with at the moment (since you're writing raw DB-specific SQL). There might be other methods available for data movement as well.
More info available here: MSDN