Find My Cover uses Amazon for finding the covers. Amazon is already supported by MP3Tag.
You could also use Amazon Cover Downloader and add it as tool in MP3Tag with something like "--acd-keywords=%artist% %album%" as command line argument.
Edit: Josher's iTunes cover search is identical to this AFAIK.
A different website doesn't help anything. The way Mp3tag presents the results does not depend on a website layout.
The web framework just doesn't offer more advanced possibilites to show covers.
If it was possible, all scripts would already present the covers with previews in one window and all that sutff.