I’d want to introduce the tool across the company but I don’t trust people to remember that it shouldn’t have sensitive information sent to it.
Basic level of security: Before showing someone the email, ask them to click on a magic link sent to their inbox. This would include a domain check to ensure that only someone from the Moogler's domain is allowed to see emails, i.e., if the initial mail was Moogled by jane@example.com, only someone from example.com will be allowed to later see that email.
More advanced options: An entire authentication and authorization system could be created around this.
Self-hosting: I could also set you up to self-host this solution.