Hide specific pages from search results

We have certain pages that are accessed from outside of our site, but which need to be invisible in search results. I’m using a plugin that adds noindex to those pages. Between that and changing the filename, they are no longer showing up in external search engine results. However, they are still showing up in the internal site search (search box at the top of every page), filename change and all.

Is there a way I can force the removal of specific pages from the internal search results?

Since these are pages (not posts), I’m not able to assign them a category and simply exclude that category from the results. And since most of our site is pages (not posts) I can’t just exclude all pages. It wouldn’t work to add a password to the pages, since they need to be easily accessed by those who have the link to them; and for the same reason, it won’t work to simply change them to draft status.

Here’s what I’ve already tried:
– Simply Exclude plugin (doesn’t seem to work at all)
– Positioning the pages to exclude under a special parent page and giving that page Private visibility.
– Exclude Pages plugin (works for menu page listings but not for search results)
– Easy Noindex Nofollow plugin (helped with external search engines but not with WP site search box)

Any help with this would be greatly appreciated. Thank you!