Container identifier portable across machines (profiles)?

I’m trying to migrate a list of containers and re-create them in another machine (another profile). However, it seems the cookieStoreId is not portable across machines. The contexualIdentities API doesn’t seem to allow setting the cookieStoreId of a new container and it’s assigned arbitrarily at container creation. The container name is not unique and it’s not used in the tabs to link to the container. Tab uses cookieStoreId for container identifier.

What’s the best approach to migrate containers and tabs across machines and preserve their association?