You could try small pellet food. Lobster eggs might also be an option as they're tiny (probably 1mm at max) and these stars seem to prefer very small food sources. The lobster eggs normally come in frozen sachets and just about everything in my tank went nuts for them. You could try defrosting some and using either a pippet or a dosing syringe (probably the better option), blow the eggs gently into the path of the starfish or, if you can, directly onto the tiny suckers. Shutting off powerheads might be a good idea while you do this. To give you an example of how small the food sources were, I remember mine actually used to surface/skim feed. It was always up the top of my tank with a couple of legs breaking through the water, filtering the surface film.
Feeding them direcly may be your only real option to keep these alive successfully in that tank and I'd even go so far as to recommend them as a species specific or kept with other tank inhabitants that won't impact upon their diet options. Despite there being an apparent abundance of algae, pellet food and other food sources, the startfish will be out-competed by shrimp, hermit crabs and snails, as they all move faster. I only rarely fed mine directly, mainly as it often was difficult to do. The starfish was often behind rocks and inaccessible, so in my ignorance, just let it be. After several months, mine died. It developed an open wound which never healed. Quite a common ailment with Linckia. Whether this was due to an infection, parasite, malnurishment, injury or a combination, I don't know. Once the wound expanded, the hermits moved in and started feeding upon it. After that it was game over.
The starfish would probably be ok in a large tank, with a lot of rocks and a carefully considered ratio of snails, as I suspect that these are probably the main rivals for food sources - especially the large mexican turbos. I had a 3ft (180L) tank, with nearly 30KG of LR. Personally, I would not keep one again in anything smaller than a 5ft, with lots and lots of LR. I know that may sound extreme but, so many of these creatures die within a year and I think it is largely due to ignorance of the creatures requirements.
I'm not saying that they cannot be kept and you may be able to keep them in that 2ft cube for a long time. However, I believe it will be as a result of diligence and direct care. If you are going to add other inhabitants to the tank, like snails and hermits, I'd keep the ratio lower than normal for a tank that size and maybe avoid snails like astrea and trochus, in favour of vibex which will be more interested in your sandbed. With the hermits, maybe avoid the micro species like the blues and mexican reds and go for tibcans or blue knuckles, that tend to eat slightly large food sources and keep them at a lower number than you normally would for your tank volume. Again, this may be considered overkill or pedantic but, I believe that it at least would give the starfish a much better chance of survival.
Cheers,
AK