There is no such thing as a "partial relational match" (which is pretty much what you're doing). I would say that your best bet would be to go ahead and do the Matching Records import, then see which ones did not get updated. That will be little tricky, because they would no longer be in the found set. You'd need to save the IDs of the original records, then compare via the matches ones.
So then you'll have a hopefully number that didn't match. Now what to do. There's various ways to proceed. Other than manually looking at the files, you would need to use some external tool to at the very least get a list of those files. If you had a list of files that matched, vs. ones that didn't, you could use a Loop in FileMaker and various tests against the file name to see if it was "close enough".
There are other tools, such as AppleScript, which can do "contains".