I'd suggest basically the same thing, using the old tank water to hold the established rock. Once the tank is drained, remove any sand and pitch it to prevent any excess food/poop from being brought into the new system.
Once it is light enough to be removed, do so. Take it outside and hose down to clean out at your leisure.
Before putting the rock into the new tank with the fresh water, dunk it in the tank water and even give it a light scrub if you want to to further prevent any nutrient sinks from coming into the new system. You can then add the sand into the system using a piece of PVC
to help avoiding any sandstorms.
Once everything is settled toss in the livestock and enjoy.