You're looking on the wrong side of the map. Boats to points east depart from Labuhan Lombok on the eastern side of the island, as clearly labeled in the map you yourself posted (!), and all travel agents and operators in Senggigi, Mataram etc ship you across there by shuttle bus before putting you on the boat.
That said, if your aim in this exercise is to cut costs, I think you're barking up the wrong tree: any direct cruise from Lombok will by definition be expensive. The cheapest way to do this is to cross from Lombok (Labuhan Lombok) to Sumbawa (Poto Tano), cross Sumbawa by bus, and then find somebody going to Komodo/Rinca from Sumbawa's eastern port of Sape.
The sane way, though, is to fly to Labuanbajo and start from there, and it's not going to cost much more when you figure in the cost of accommodation (and aggravation) involved in the alternative.