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I'm guessing that the "massive 'sparse matrix'" is being left as an Excel file and not a Tableau data extract? That can deal with much larger volumes of data.
In any case, to do this kind of analysis in Tableau you will need to pad out the data. There are a variety of ways to do it, I assembled a number of related posts in http://community.tableau.com/thread/121505?start=0&tstart=0.
I essentially aggregate the data I am looking for from separate MySQL instances at each location into a single spreadsheet, and then I do import all the data into Tableau.
Not surprising this was a hot topic a the last conference.
Ill read thru all those posts and see where it takes me.