You should be able to override all the styles just with your own custom CSS either in a theme or plugin. The two primary selectors to target the autocomplete are:
ui-autocomplete: The menu used to display matches to the user.
ui-autocomplete-input: The input element that the Autocomplete widget was instantiated with.
And there’s more info here: http://api.jqueryui.com/theming/css-framework/
Indeed but the .ui-autocomplete gets appended to the bottom of the page, right before </body>, so there’s no way to contain the width unless I set a fixed width. Problem with that is that since the site is responsive, the form width changes.
I may end up using wp_deregister_script for your js, and register a copied version with the addition args.
It’d be a nice feature to have – the ability to specify which element you’d like your autocomplete list appended to.