Is there any way, when adding a dimension, to default all LTS to a specific logical level?

Nope.

As Gianni and Christian have said, a model this size is probably not the best approach in an ideal world.

The only option you have is to look at a script-based approach. There is a supported API for modifying the RPD metadata: https://docs.oracle.com/middleware/12212/biee/BIEIT/bi_server_web_services.htm#BIEIT3253 (and here too), but as Gianni and Christian have also said, it'd be pretty easy to screw things up, doubly so given the size and complexity of your existing RPD.

You can see an example of it in action here : https://www.rittmanmead.com/blog/2015/09/using-the-bi-server-metadata-web-service-for-automated-rpd-modifications/ Note that all I change in that blog post is the value of an existing repository variable. To add in additional content, with the issue of GUIDs etc, gets very hairy indeed.

tl;dr : sit tight, and keep clicking, unless you're feeling brave