Thanks for this.
The reason why the CLI client incus needs to specify the project, then perform the export, is because it’s designed that way.
I believe that it should be possible to use the API to perform the exports in a way that you do not need to specify the project first. This would require writing the appropriate script.
As is shown below, you need to get the fingerprints of the instances, and then you can export each one without specifying the project.