Sorry to waste people's time with this post.

In "Add/Remove Programs", I did indeed remove a file I believe was called something like Microsoft Office Compatibility Pack.

However, I did not have a check in the box "Show Updates" in Add/Remove Programs. When I put a check in there, sure enough, there was an update for MS Office 2007 compatibility. Once I removed that, I was then able to install the latest update "FileFormatConverters.exe".

Now I can open xlsm, xlsx, etc., in Excel 2003.