I eventually found that this thread from 2012:
http://scn.sap.com/thread/3143010
pretty much had the answer. I was using Oracle 11g and MII V15. I did not need to make any driver changes.
All I had to do to get this to work was change this line:
xmlData := '[Param.1]';
to this:
xmlData := [Param.1]; -- no single quotes
and, on the Parameters page of my Query Template, I had to check the Use Typed Parameters checkbox and choose the String type for parameter 1.
After making the above changes I was able to pass a string that was over 1 megabyte without a problem.