Ah, never mind. I figured it out. My current Winzip handles it just fine, turns out that it was just the way I chose to create the file.

What I did (which didn't work) was to use the CTRL key in my development directory to multiple-select some of the skin subfolders and the EXEs and the readme. (Had to do this so it didn't pick up all the source code files at the same time.) That's what gave me the duplicate file name error.

If, instead, I create a folder called "EmpegFace", copy all the files and subdirectories into it that I want, go to that folder's parent, right click on the EmpegFace folder and select "Create EmpegFace.zip" from the right-click menu, then it all works perfectly.

I could swear I knew this at some point in my lifetime, I just got somehow stupider between then and now.