Don't drop the existing table.
Create a new, test (dummy) Quality table UNIQUEly CLUSTERED on ( Quality_Date, Quality_ID ).
CREATE TABLE dbo.Quality_Test ( ... )
CREATE UNIQUE CLUSTERED INDEX QUALITY_Test__CL ON dbo.Quality_Test ( Quality_Date, Quality_ID )
Create the clus index BEFORE loading the table. Don't create other indexes prior to load.
Load the _Test table in batches, in current clus key order, from the main table. Make the first batch larger than the rest, and be sure to specify WITH (TABLOCK) on the _Test table while loading. You can specify WITH (NOLOCK) on the original dbo.Quality table.
Once it's fully loaded, you can create the other indexes if you'd like. Don't create any FKs, you don't need that hassle right now.
Finally, test selected slow queries by changing table "dbo.Quality " in those queries to "dbo.Quality_Test ".
Yeah, that takes some disk space, but is otherwise not disruptive of your current environment.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."