Is there any way to speed up a query with 3x UNION on the same large table?
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.