Thank you both so much-- that did it. I'm now returning the modified date just as I was trying to do. I appreciate your input. As Geoff noted, the trouble lay in my not including the sites/sitename/ prefix. Here's the assignment that causes the query to work:
Thanks again, gentlemen!
actualFileName = "sites/unit/subUnit/Shared Documents/folder/subFolder/FileName.docx";
The query itself didn't change, so the problem was completely due to the formation of the path in actualFileName.Thanks again, gentlemen!