I have a dedicated electrical circuit for my aquarium, so any time I change tanks everything must be done all in one shot. I have both downsized and upsized and I always used the same rock and sand and much of my saltwater. After you have removed livestock, coral, rock and 2/3's of existing water, take the opportunity while the rock and coral are out to vacume your existing sandbed well before you move it into the new tank.
I would have a brute can of freshly made saltwater ready. When the new tank is in place put the new sand in and then your existing sand. Add just enough water to have your sand submerged. Now build your aquascape how you want it. When you have it done put in a plate or bowl to deflect the pumped water from trenching/churning up your sandbed. This will help a lot with initial cloudiness. Fill the tank half full and add coral and livestock. Also add the original tank water, the coral and livestock. Also I always add biospira to help offset the mini cycle that will be coming.
Add powerheads for circulation and aeration while you finish up plumbing the tank, along with a heater to get the temperature back up. Both coral and fish tolerate cooler temps well however.
When everything is done make sure you test for ammonia every other day and be prepared to do water changes to bring ammonia back down. It does not hurt to have Prime on hand, although remember that this will give you a false reading, so keep doing 10% water changes. My experience is that the tank settles down in about 2 weeks and is fully cycled. Don't add any new livestock for about a month however to give the new system a chance to stabilize.