After 3-4 hours of studying the uploader.js I found the NumFilesShowQueueUI property which, if set, gives me exactly the functionality I asked about in my previous post.

 

The funny thing is that this property is NOT documented anywhere, nor is it part of any example... It isn't even programmed to receive any value in the include_phpuploader.php with let's say the following code:

 I wonder why is that so, and how is somebody supposed to know about this property...