I am creating some advanced search functionalities, part of that means I removed the default search input with name="s" which WP_Query uses to set is_search to true and replaced it with a multiple select element with name="terms[]". I’m following Milo’s advice in the comment here (http://wordpress.stackexchange.com/questions/140793/removing-s-from-search-with-custom-parameters) but I have thus far been unsuccessful.
It should work (passing search.php, not base-search.php) so if you’re getting redirected to the home page then it’s probably the logic in nice-search that’s causing the issue. It’s all towards the bottom of lib/cleanup.php but you can turn it off in lib/config.php.
You mentioned that you were redirected to the home page and that code is a fix for empty searches redirecting to the home page. I’m guessing that the two are related because invoking the wrapper how you are doing it should work.
Commenting out the roots_request_filter still results in being redirected to my project’s homepage, even when I locate search.php. If I change the priority of my template_include to 999 then I do end up on the search results page but without the wrapper (and the search query is lost).
Changing s to terms[] disables the roots_request_filter in the same way as commenting out the function would, as it’s looking for a form that’s no longer being sent.
If the search query is being lost then there’s an issue. Personally, I would switch back to one of the default themes and see if you can get the search working correctly before trouble shooting this.