It sounds like you have made some progress on this. It should not matter where you are applying the upload, so long as the paths to the folders are correct it should work out. You should be able to use the same page as you get a successful result with in your root in the admin folder, then just update the paths so they are pointing to the files correctly.
The include code with the ../ in the front of it is looking the the parent directory. So if your admin folder is in the root of your site and so is the webassist folder the paths for the includes in the pages that are in the admin folder should have the ../ in them. So long as the files are in the location specified it should work for you.
Please post back with more details about what you are experiencing with this after making the updates to the paths and uploading the folders. If you continue to have troubles with this let us know and I will open a ticket for you.