Joe, thanks for the quick reply! It wasn't the exact answer I needed, but it got me going down the right path.
I do not have any fields designated as the Document Name, so by default it always uses the file name of the document when indexing through the Docuware client. So this got me thinking. If I'm setting the index values FIRST before I upload the document, then Docuware doesn't know the filename at the time of the record creation.
So, I changed the order in my code to send the file first, THEN set the index fields, and it works! File name becomes the Document Name as it should.
Thanks for pointing me in the right direction!