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I'm afraid this is still a permissions issue. Akeeba Backup simply uses PHP's DirectoryIterator to open the folder for enumerating (listing) its contents. PHP asks the Operating System to do that. When the Operating System says PHP is not allowed to open the folder for listing its contents PHP throws an Exception (a kind of catchable error condition). This is what we catch and report back to you. In other words, there is nothing our code or even PHP itself can do.

Note that last year I had written a blog post about setting up an IIS installation for local development (https://www.dionysopoulos.me/iis-development-server-for-php-on-windows-10.html). While writing it I had noticed a few things:

• It is important to give the correct permissions to the folder of the site for the specific Application Pool user, not the IIS primitive users. You need to give Read & Execute, Read and List Folder Contents for directory iteration to work. The first two privileges would allow a Joomla or WordPress site to run since you are always accessing a specific file (index.php) but not iterate it. Unlike *NIX systems like Linux where the execute privilege allows you to iterate the contents of a directory, Windows has a specific privilege.
• You need to make sure that any symlinked files/folders or directory junction targets have the same privileges. The privileges are evaluated at the leaf node of the filesystem, not the symlink or junction point.
• Make sure the site is assigned to the same Application Pool.
• Make sure PHP runs as FastCGI. I don't think you can run it in any other way on IIS but it's good to make sure anyway.
• After making all changes you need to restart the site in the IIS management console. Otherwise the site is still running under its default Application Pool and you get all the wrong permissions.