Thank you for providing us this solution. I was looking to this issue for several weeks. My query_stats table is also very big: 30,000,000 rows for only 1 managed instance with 7 days data retention.

I put page compression on the table, and changed the frequency of the data collections to 120 sec.

Tried to add indexes from the DMV missing indexes, but nothing helped. I faced the same problem as you, having to wait more than 10 minutes to get the query details report. Now with the 2008R2 version of rpt_query_stats, I get it in 5 seconds.

You make me very very happy today. FYI, my SQL 2012 version is 11.0.3393.