Disclaimer: We are required to set the org-wide default for contacts to "Controlled By Parent" for reasons unrelated to our issue.
I am trying to determine if there is a way to hide some Contact records from being visible to all users, except for maybe SysAdmin. We originally had a plan to set Contacts org-wide default to "Private" and then set up the sharing rules based on criteria. However, because of the disclaimer above, we can't set any sharing rules at all at the Contact level, since all rules are set at the Account level. And we definitely don't want rules at the Account level, since our users should be able to see all the accounts, but not all of the contacts under the account.
Is there any other way we can hide these Contact records from being visible in the global search and on Account records without using Sharing Rules? I have thought about changing the Owner to a dummy user and building special permissions around it, but nothing has really come to fruition. I am also pretty flexible on what method we use to hide it, it doesn't necessarily have to be user-based or field-based, just whatever works best and is fairly quick to do.
Thanks in advance!