I can confirm the following:

Our ship was outfitted with Invincible II Hull, Enterprise Rigging, Odyssey Forecastle, Enterprise Aftcastle for these trips. I fully repair the ship before every trip.

Our first visit to sector 12 at rank 48 resulted in the discovery of sector 16.

Our first visit to both sectors 15 and 16 (same trip) at rank 49 resulted in the discovery of sectors 19 and 17.

Our ship is currently exploring both sectors 19 and 17. We are hoping for the discovery of both sectors 20 and 18 tomorrow if we are lucky. I will report back.