Each Firefox locale comes by default with several search engines that can't be uninstalled, you can possibly disable them via "Settings -> Search". Full list:

• resource://search-extensions/

I'm not sure why you have two Amazon search engines.

I tried unchecking the unwanted items and restarting Firefox (just in case) but they all persist. I also tried Removing them with a restart, still no help. It seems this procedure only controls what appears below the search bar.

These are "internal" add-ons that are included with Firefox by default. They are the way that we use to define and ship the application provided search engines, they are basically just a small file that defines the settings for that search engine and its icon, there's no functionality within that.

Having the add-ons will not affect your Firefox, if you have removed the search engines then they won't be used for anything.