I seem to have stumbled on a workaround that does not involve mucking with the metadata in my .mobi files. This solution will enable you to load your .mobi books onto the Paperwhite and have them show up categorized as books with full covers and NO "Personal" banner ruining your cover.
The only catch is that you have to be able to share your Calibre library on your local network so that you can access it via the "Experimental Browser" on the Paperwhite.
Here are the steps:
1. Enable "Sharing over the net" in Calibre preferences so that your Calibre library is available on your local network via any web browser.
2. Make sure your Paperwhite is connected via Wifi on your local network.
3. Go to the Home page of the Paperwhite, tap the little "Menu" icon in the upper right corner, and from the drop-down menu, tap "Experimental Browser."
4. In the URL box, type the URL to your shared Calibre library. (After the Calibre library page loads, you may also want to bookmark this page for future reference: tap the "Menu" icon in the upper right, and then tap "Bookmark this page.")
5. In the browser, find the book you want to load to your Paperwhite, and tap the .mobi format link. Confirm that you want to download the file, and then you'll get another confirmation box that the file downloaded. Just click OK.
6. Tap the Home icon in the upper left and your book should be in your Paperwhite library, with the full, non-generic cover intact, categorized as a Book, and with no "Personal" banner.
So far this has worked for me, but only with .mobi files. When I tried it with .azw3 files, it just showed the generic cover icon. No idea why this might be working, but I'm not complaining!
I realize that it's a lot slower downloading the books one-by-one than being able to sync a bunch of books directly via USB with Calibre, but it's worth it to me to get my full covers and to have the books show up as Books on the Paperwhite.
I'd be interested to know if anyone else can get the same results with this method, as this would be a much simpler workaround than the complicated metadata editing suggested in other topics. But for now, it's working for me at least!