I've had starfish successfully in a 13.5 gallon, and I probably have the exact tank you are talking about so I had to target feed. I leave very small pieces of white shrimp or fragments of freeze dried krill that are dosed with amino acids meant for corals slightly buried in the sand directly in theirs paths so that they can intercept it. Target feeding them by pushing it into them or placing them on top of it can often scare them away. I have found that starfish have a big appetite for a piece of food that has a drop of something with an amino acid base in it, practically running towards it. It kind of makes sense, because corals like amino acids to develop their calcareous skeletal structure, and starfish also have a calcareous skeleton. If your tank has any amount of film algae on the sand they will eat this as well. Most of these kinds of starfish in my experience are omnivores, and cannot survive with only algae or only meaty foods alone. If your tank has no source of algaes, you can break up small pieces of algae pellets or hikari herbivore and leave them in the sand bed for it to find. Keep in mind, small and few pieces because you don't want any big nutrients spikes.
Also, my tank originally had two starfish, and one died to sensitivity of a product called reef buffer. Just sharing because I believe starfish don't like this product in small tanks!
This is my starfish in a 13.5 gal reef tank and he has successfully been living here for quite a while. As you can see, he loves to eat my beautiful plants. I have had great success in target feeding him and he has never shown any interest in my anemones or corals as a source of food. I should however probably start feeding him algae pellets again, as my caulerpa isn't meant for chomping!
After detaching the leaf that has already been damaged by his digestive enzymes so he doesn't try to ball up more of my plant, I can place it in the path of his movement after returning him to the sand. He will take hold of the leaf and ball it back up again so he can eat it.