It will work to a degree.
I WOULD NOT recommend moving all the sand NOR the mixing of the sand, as this will cause lots of unwanted material to be dislodged and put in the water column causing a possible mini cycle. Unless you are going to skim/filter it, a lot. Plus removing all the sand knocks a medium size hit on the bacteria for filtration.
I mean if you are going with just NEW sand (as in the addition you talk about) then it will be good. Just checking on if you are moving the sand and adding sand or just doing NEW sand. While some people do not really talk about cycling new sand that much, mostly talk about rock, there is some cycle with the rock and getting it live and populated with bacteria.
The existing live rock you have will be good. Just make sure parameters are as close to the same from the existing tank to minimize any shock or die-off.
Keep the LR wet/submerged or limit the time out of water to less than 2 minutes.
If you have some GHA TAKE CARE OF IT NOW before putting it in the new tank, since you will already have it out of the water.
On the rock move:
Schedule it during a water change if you can. (Yeah, but you need to be ready incase the new tank has a problem.)
Do a partial water change (maybe 10 gallons or so) and put it in two 5gal buckets.
Take one of the rocks and put in bucket A. Take a scrub brush, the one with nylon bristles, and scrub the ENTIRE rock twice, while in bucket A. Swirl rock around and then take out and put in bucket B. This will wash off anything BAD (GHA) that might have been brushed off. In bucket B just swirl around a few times to wash off anything that was missed, no scrubbing in it.
Continue with a few more rocks.
When time to do it again, do another partial water change.
At the end of each 'move of a few rocks' finish the water change so that you collect anything that you knocked up taking the rocks out. This way when the fish are inside they still have good water.
Now a BIG part to remember. Each time you remove a rock you are cutting the bacteria down for any filtering. You will really need to keep an eye on the fish. As you get to 1/2 the rock moved... You need to make your next move the last move. The bennificial bacteria will have increased some in the absence of the other rocks, but normally not enough to handle a full load, of course this all depends on what you have in the tank already.
A quick plan:
New water
New sand (wash it)
Seed the sand with maybe 10 cups of the old, if it is still good and color matches.
Take one rock also to help seed.
Let set for a bit. (a week or two)
Take one or two rocks a week (depending on how many rocks you have) just make it so that 1/2 your rock is moved by LAST move date.
Do a little fake feeding to keep the bacteria with something to eat.
You are on the road to a good upgrade.
Check with your fish compatibility with the tangs and other occupants.
