I think it's possible to provide the option of having either a regular toolbar button ("browser action") or an address bar button ("page action") but unfortunately, there's no way to move it, it would need to be changed through the Options page (after writing all the new code).

Do you have a suggestion for a new icon? You can send it to me at jscher2000@outlook.com, or create a new issue at https://github.com/jscher2000/cache-favicons-for-bookmarks-extension/issues