Private Profile Field Viewable Only to User?

[wonderfulwat]

I want to store sensitive user information (ie. a member's physical address which will be used for shipping) that is editable by the member and viewable by admins.

Settings I've Tried

Add New User Profile Field Multiple-Line Text Box
Private Field: Yes.
Usergroup Can View Private Custom Fields: Yes

The problem with this set-up is that ALL members of the same usergroup can now view each other's mailing address. That's a big security concern.

How can I make it so only the current user and admins can view/edit a profile field?