how can I customize url and search fields to remove search engine dropdown?

How can I customize url and search fields to remove the search engine dropdown, and ideally make the URL fields ONLY work with URLs and the search field only work with my default search engine? A recent update has completely broken my muscle memory: I'm used to typing Cmd-L to move to the URL field, then a single tab to move to the search field, where I immediately start typing. Now, that single tab moves me to the search engine dropdown, which I don't even want to use, so every time I try to search I have to stop and back up and it's badly affecting my workflow. How can I either change the tab order or just get rid of the dropdown completely? If I want to use a different search engine, I can always just go to their page instead of using the search bar. Also, is the URL field now exactly the same as the search field? I really want them to behave differently - I don't want to touch search if all I'm doing is re-visiting a URL in my history. Is there a way to have a URL field that ONLY works with URLs and avoids search, and a separate search field that works with my default search engine? Thanks for your help.