How can I use Group Policy to enforce and append security groups to the local administrators group?

What you're describing is called Restricted Groups, and, you got it -- it's seemingly not possible to make Restricted Groups' most useful feature be "additive" (or, more accurately, "augmentative.") That is, most people want to use it to add _additional_ members to an existing group. But that's not how the "Members of this group" function works. Rather, it "rip and replaces" existing members. So, it's not ideal in every situation.