Can you try either of the following?
1. Using the REST API, query view data
2. Bring up the report URL and append .csv onto the end of it and see if this downloads what you want. If so, maybe you can do this programmatically.
We're aware of appending csv to the end of the URL, unfortunately csv isn't an acceptable business solution for us, so if we used the CSV url, we'd then have to run it thru an XLS converter anyways. That's our final option if we can't figure anything else out.
It looks like the REST API will also return the underlying data, not the pivot grid?