Is there any way to speed up a query with 3x UNION on the same large table? Assuming that the following query is legitimate and executes successfully, is there any way to speed it up?

SELECT foo from T1 --T1 is a huge (&gt;5e6 rows) table with no indexes
UNION
SELECT bar from T1
UNION
SELECT baz from T1
UNION
SELECT qux from T1


The four columns shown above are all of type nvarchar(128), non-sparse and nullable. I am using SQL Server 2008. Thanks!

EDIT: Provided more info. I cannot add indices because it is a Stage table. Also, removing the DISTINCTs; I totally forgot about that. 

Phil: How do I consolidate this into a single query?
You can certainly project foo, bar, baz and qux in a single scan (SELECT foo, bar, baz, qux FROM T1).  A CROSS APPLY TVF can transform each row (4 columns) into 4 rows (1 column) and then apply DISTINCT on top. If the original plan had 4 scans of T1 which would dominate the cost, this may be better.