Hi JonClay,
Is it possible to set these templates up as personal templates for each user?
Is each user a separate template? Or do different business units have different templates and users in the same business unit share one template?
(1)If you want users to see only the email templates they have created themselves, you can make users select 'Individual' permission level:

(2)If you want to use 'business unit' level email template:
Select 'organization' permission level to create email template and set privilege of the 'Email template' of security roles that assigned to users.
Settings > Security > Security roles:
You can refer to the following thread to set correct permission:
only users with Sys Admin rights can amend email templates:
--Remove the "write" permission of email template from all security roles assigned to the user (except the administrator role)