Crinoids would be as specific as possible...I'm not sure I've ever heard any reliable success stories with them even lasting months except for 1 or 2 in Coral Magazine because they're so particular about the particle size of their foods along with what the food is as well of course.
Yeah, crinoids have specific particle sizes for foods they'll catch and eat (and to make matters worse, that specific size varies from species to species), but the real issue is that - much like with current "impossible" starfish - we don't know what they get their nutrition from. We know what some of them eat, but, like some species of filter feeding bivalves, they'll eat literally anything (including inedible things like sand and plastic beads) as long as they're sized properly. For obvious reasons, sand and plastic do
not provide good nutrition to filter feeders, but they still consume these things. So, the real trick to keeping these guys would seem to be figuring out what they derive nutrition from.
Unfortunately, this is easier said than done, as they consume a huge variety of different particles, and some of the things that they are speculated to derive their nutrition from would be incredibly difficult to provide with any sort of consistency (such as sperm and eggs from broadcast spawners, or veliger stage snails). Other things that might provide the necessary nutrition may be easier to find (though not all of them would be on the hobbyist level), but there are so many of them that it could end up requiring dozens of different tests with a number of different specimens of the same species to figure out if any of them are viable options. Plus, it may be that a combination of things are needed to provide the proper nutrition, and that makes it substantially harder.
Once we have figured out what they get nutrition from, then we would need to figure out how much of it they need and how frequently they need it.
If we can figure out those two things, then we should be able to keep these stars without problem (or at least the people who care enough to become educated on them should be able to), but, until then, it's really just going to be trial and error with most people failing and a few succeeding.