I think what you ask its not so complicated to accomplish in a script, see for example Entity Migration Script: Hierarchical Data Transfer Between Databases which is not your use case but somewhat related.
You may be lucky this time, last week I did some work in creating pattern template maps as I call it, which allows users to clone an entire project tree. The functionality goes both ways: either create a tree from a template map, or save an existing custom tree as template map, with one click.
In the coming week I will share example code. This is assuming the Project, Section and Task are the databases that are used each time, but the entities and how they relate is unknown thus needs to be determined dynamically by the script.
Related but maybe interesting also: I’m currently also working on a databasemapping system that allows a script to use a custom set of databases in a preconfigured relation cluster, based on the databases that a user selects. Say you have 50 databases and want a custom mix of a few of those in a custom tree, the script can do that, as long as fields used are of the same types and show a corresponding pattern in their names.
I think what you ask is a common need when branching or forking a project, and is worth to be a Fibery feature, but the question is if the value proposition of Fibery, the product killer feature, gives what you want priority over its developpment needs, as like described in Fibery 2.0 that focus on insight through relationships.