i just did this 2 weeks ago. i chose to do it all at once. here is what i did:
i took all of the water out of the tank except for the water that was in the CC, so all but about 2 inches of water. i put this water into a LARGE rubbermaid tub , along with my LR and fish. i transferred the LR to the tub as soon as there was enough water for them to be totally submerged.
i then cleaned out all of the CC, which is not fun at all, cleaned out the entire tank. dried it out, then added the LS into the tank. then i took a CLEAN trash bag an laid it across the top of the sand and weighted it down with some pieces of LR. this is so the water will not stir up the sand as much when you pour it back in.
then water goes in about half full, trash bag comes out, the rest of the LR goes in and is arranged. livestock then goes in as well,and the rest of the water is put in. this is a great time to do a water change as well.
this worked out well for me, cloudiness was gone in less than 2 hours, and no caualties to the livestock as of yet. i got this method from a post on here a month or so ago.
hope that helps ya!