Per several other questions I've answered similarly, just by adding a "STRAIGHT_JOIN" and slight restructuring can help. The query optimizer will actually try to think for you with respect to all the tables, try to find a table with less records and join that to the larger thus causing total chaos. This happened when I was doing gov't data querying of 14+ million records with lookups to 15+ sub-tables... Very similar to what you have going on here.
It took a query that was running 30+ hours on a dedicated, stand-alone server and hung it, down to under 2 hours... Try the following.
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