Hello Jesse,
Thanks for posting in! Just for future topics, self responding or bumping your post pushes it back in our Queue system so it takes longer to respond to.
Your php code is incomplete and invalid. There is no such is_faq-category() function exist. This condition will not work.
Keep in mind that this particular customization request is outside the scope of our support as this is not related to an issue with the theme and instead has to do with your customization of it. If you are not familiar with customization, it is best that you find a 3rd party developer to do the customizations for you.
To get you started with, we would highly recommend that since you are using Integrity stack, please copy the _landmark-header.php file from wp-content/themes/pro/framework/legacy/cranium/headers/views/integrity. You will have to upload this file into your child theme’s folder wp-content/themes/pro-child/framework/legacy/cranium/headers/views/integrity. Using the right condition, this is the right file and location where you can insert your custom post type landmark header.
Instead of using is_faq-category() which is not correct, you will have to use is_post_type_archive as a condition which you can learn more about in this codex:
If you have any further questions about the theme, we are more than happy to provide you with assistance on these inquiries.
Thank you for your understanding.