MCF has hit the nail on the head.
What are the tank parameters? especially pH, specific gravity, alk? Nitrate levels?
Multiflora's are perhaps the 'best' of the Linckia sp stars, though, as noted, none are particularly tough. But I think they would be OK in a 75g, assuming there is a good amount of LR in it. We have another member here who has them in a 75...perhaps a search for Linckia multiflora will help.
The exposure to air thing is a bit of an old wive's tale and I wouldn't worry too much about it. Again, look for one's that are firm, good color, no 'melting' or mucusy spots, been at the store more than a fea days (keep in mind that they will deteriorate up to a month after introduction, if suffering from osmotic shock.