I dealt with this issue when I upgraded from a 75g SPS reef to a 180g. My thought process was that vodka is a carbon source for an in situ bacterial culture in my tank that feeds planktons that in turn feed corals and uses up N&P in the process. The filtering bacteria are on the rock and in the sand, but the bacteria that eat vodka are in the water column, like in a plankton reactor. In my established 75g i assumed that bacterial population was in the stationary phase meaning as healthy and as crowded as possible. Too much vodka and it would lead to a bacterial bloom, then move to the dying phase (too many bacteria, not enough food/nutrients) using up lots of O2. If I were to double the water volume, the bacteria would move back to the exponential growth phase as now there is more room to grow, assuming a steady food supply. So when I moved to the 180g I continued the same amount of vodka, and aimed for final total daily dose of approx 2.4x more (180/75 = 2.4).
This was based on the assumption that the entire bacterial population would be transferred to the larger tank. This could be affected by (to name a few)feeding, skimming, carbon, ozone, cycling- which would probably greatly decrease the bacterial population. Obviously the new tank would need to be fully cycled with any new sand and rock. Also, the old tank would have to avoid starting a new cycle as the goal was to bring over all the water, sand and rock. I did this by cycling the new tank for 6weeks, and moving 1/4 of the old live sand to the new tank every week until the 75g was barebottom (this meant siphoning out the very last granules of sand). I started up dosing vodka into the new tank after it completed its 1st cycle, while maintaing the dose in the old tank. Then when both tanks tested zero for ammonia, nitrite and nitrate I brought over all the live rock, livestock and all the water. At that point I was halfway to the max vodka dose in the new tank, so I continued to ramp up.
This was a pain in the ***. Not to mention obsessive-compulsive.
You could simply cycle your new tank and transfer over all of the old tank in 1 day, restart the vodka and be done with it. I wouldnt bring any old water or live sand (except for a couple cups to seed). I would feed the coral heavily, test parameters daily for the first few weeks. If you use ozone, you can use the ORP reading to help.
BTW, this would be the perfect opportunity to re-quarantine and treat all the fish.