Answer
Unpublish and then Publish the Custom Logical Unit again in EE — this regenerates its auto-generated Custom Projection, which then reliably reappears in Aurena's API Explorer. Note that creating the Custom Logical Unit itself still has to be done in EE (this isn't yet possible directly in Aurena); only the resulting Custom Projection can either be auto-generated from EE this way, or alternatively built manually in Aurena.