Prevent users from seeing Executive Recruiting Type job requisitions?

How can we create a role like Recruiter View All, but prevent users from seeing Executive Recruiting job requisitions?

Context & Description:

Right now, the Recruiter View All role lets users see all job requisitions. We want a similar role (for example, “Non-Confidential Recruiter View”) where users can still see most requisitions, but not the ones with the recruiting type as Executive Recruiting.
So basically, the new role should work the same as the existing one, except it hides executive-level requisitions (Recruiting Type == Executive).