If you transfer the live rock I would be sure to add 50-75% of the total water volume from your existing setup and the rest can be made up of new water. So you could do a 10gl water change on the 75gl and use the old water in the new 20gl.
The sandbed will go through a diatom cycle from the added silicates of the new sand. This is normal though so expect to have some brown film on the new sand until it's a healthy live sandbed.
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