Finally got it figured out.
One must first manually change the connection in a report.
Then use the utility referenced by Bhushan to generate the code for changing connections.
Then modify that code to make it more generic for use at runtime, passing the report file, connection parameters, etc.
The generated code changes the connection info for the specific table(s) in the report that it was run on.
That portion needs to be changed to loop through all of the tables in a report and reset each.
This project does not contain any subreports, so did not need to handle that aspect.
