Unfortunately, using Javascript doesn't seem to work, because the browser fills in the form fields before the Javascript is run.
In case anyone else needs to do this, the solution is to add a hidden field with the id "autocomplete" and value "off" as the first field on the form. It has to be the first form field, though. You will also want to add 'save_field' => 'false' to prevent the field from being saved in the database.