I typically try to avoid cross-linking in early implementations. I have often seen tendencies to link each circle with every other in order to overcome the pain the org experienced in their former structure: lack of information flow, bad sync on interfaces, power games who ultimately rules...etc.
A few thoughts on how I experience it/coach in practice:
1) High need for cross-linking might be a good marker for a structure that is not the most requisite regarding the orgs current needs. Rather than "circling" former teams/departments ask which work needs to live close in order to have the most cohesive bundle or work in a circle. So use the "tension" of need of cross-linking to reflect on your setup.
2) Instead of cross linking you might ask which additional perspective the circle needs to better express its purpose? E.g instead of cross-linking you could create a simple role in your circle that brings in a specific lens (filled by people holding relevant information due to other role-filling in other circles). This is sometimes enough and replaces the initial need for cross-linking.
3) The most important thing to me in practice - having seen struggles with cross-circle navigation: I frame Gov as a way to continuously create/establish clarity of where acc and authority reside. Once roles are clear (continuously beta) you can "disregard" the structure and use role clarity for highly-efficient role-to-role interaction. No matter which circle they are in. In "mature" practice the aspect of "harming" circle boundaries by walking up to roles directly becomes less relevant IMHO.
May that triggers some thoughts.