Is there anyway to lock down a project or repository so even System Admins don't have access?
No you cannot. The Bitbucker server (Stash) Global Permissions for "System Admin" explicitly stated that in their tooltip text.
System Adminstrators
Has full control over Stash - can modify system configuration properties and all application settings, and has full access to all projects and repositories. We recommend granting this permission to as few users as possible.
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