John, as a follow-up, wanted to let you know that it all works very well. I
have tweaked the code enough so that it is now part of a custom add-in I
have written, and works just as I intended.

There was one line of code that you provided which was throwing up an error
every time (Type mismatch error) :

If fileName Then

which I changed to

If fileName < False Then

and strangely, all is well with the world. Wondering what that was about?
FYI, I'm on WinXP Pro & Office 2003.

Thanks again,
Amit