SQL Tuning - String Of One-to-one Joins

I have a query I am trying to tune. It presently takes anywhere from 15 minutes to two hours to run, depending on how many records the client has. But it needs to run several hundred times, and finish over the course of a weekend. When it runs over, we have problems.

Here's the basic structure of the query:

CODESELECT ...
  FROM main_tab,
       tab_a,
       tab_b,
       tab_c,
       ...
       tab_z
WHERE main_tab.client_id = :1
   AND main_tab.unique_id = tab_a.unique_id(+)
   AND main_tab.unique_id = tab_b.unique_id(+)
   AND main_tab.unique_id = tab_c.unique_id(+)
   ...
   AND main_tab.unique_id = tab_z.unique_id(+);

All of the tables are indexed (and statistics are gathered) on the field unique_idMain_tab has an index on client_id.There is a one-to-one join (sometimes one-to-zero, thus the outer join) from the main_tab table to all the other tables.These are static tables, they're wiped and recreated - no changes, inserts, deletes.

By default, the optimizer does a full table scan and then a hash join on every single of the 26 tab_a through tab_z tables, only using the index on main_tab.

By the way I can add indexes, possibly even to the point of adding an index on some tables that would include all the fields found in the select clause on that table. But I cannot change the table structure (by, say, combining these tables together).