I didn't try yet the new ImagesToIcon,
but I did some tests, and I figured out that, if you edit the desktop.ini file within the created folder, you will be able to move/rename the created folder as you wish.
You need just to remove the path part like this:
Another thing to add, a suggestion, you can make 2 checkboxes:
[ ] Create a folder
[ ] Create a FolderIcon.ico
If user check the both 2 checkboxes, it means you need to create 2 icons:
1 hidden icon for the new created folder, within the folder like the file desktop.ini
1 not-hidden icon as FolderIcon.ico
It's always better to have an open-source code, for customization.