You can dose your entire tank with CP if you remove all inverts/corals from the tank, it will kill everything left behind, all algae..all the beneficial critters you might have.. (If you only had dry rock in there and not live rock with critters in it then you probably wont notice and it will just be like starting over).. you'll get an ammonia spike.. but after 30 days you should be able to clear the CP out with carbon and add everything back in, just test water parameters first.
-I believe you can leave the crabs behind as things with exoskeletons will survive, but with the ammonia spike you'll likely get I'd probably remove everything you can that you want to keep. Anything with a shell will need to remain outside the Display tank for 90 day though... as the ich can attach to hard surfaces... that means either moving your crabs/snails to a different tank for 90 days and your cucumber and anemone and shrimp to another so you can re-add them once the display clears... or just keeping them in QT for the full 90 days together.. (shrimp you can add to the display tank once they molt and the CP is clear)
The iffy thing here, and with CP treatment in the display tank is the tomont stage.. when they hibernate and multiply.. can last for 2 months.. and I'm pretty sure CP can't kill that.. so it might not be effective... but, if you put fish in a tank with cp in it that was fallow for 90 days or was dry or freshwater then it will kill everything on the fish and that drops off the fish before it can become a tomont.. so that is how that works to make that tank ich free after only 30 days. (realistically 2 weeks should be enough, 20 days tops)
so overall my recommendation is to just keep your display fallow for 90 days.
