Alternate ways to increase column size
If the queries that are accessing the table that need to work while you're making this change are read-only, you could create a view that has the original column and uses the function in place of the computed column, then in a transaction rename the table and create a synonym with the original name that points at the view, then make your changes, start another transaction where you drop the synonym and rename the table, then finally drop the view. If the table needs to be read-write in this time, this may not be sufficient.

This isn't strictly doing what you asked (changing main without affecting computed), but I still think it has the desired effect - minimal impact on users.