Hi Max,
It is important that you don't just transfer everything over at once. I am currently about to start this process, and I have seen too many tanks where people just move everything over at once and then about a month later the new tank crashes.
First thing I would do is move over some (maybe a cup or so) sand and some small rocks. If you can get some more good cured rock put that in also. I would not put the lights on in the new tank at first because you are going to get a nutrient spike and better to keep the algae at bay at first. Watch your nitrates as a general indicator and do water changes to keep things under control. Keep moving sand and rocks progressively over time. Then when you feel comfortable ... maybe a couple weeks or so move over you leather. Of course turn your light on and Keep watching things. I would next move the polyps. Keep moving sand and rocks over too. Watch the tank and ensure that the nutrients aren't overwhelming things and use water changes as your correction mechanism.
After you get the leather and polyps moved. I would then move the clowns over. I really should say at this point that you should keep your old tank up because if things go south you have it as a back up. If the clowns do well after a week then I think you safe to move the rest of the fish over. You may want to when you move over the other fish, mix up your rock work or scape the tank into it's final look. This should keep agression down and allow new territories to be established. This transfer should be a gradual process.
That is how I would (and will do it). Slow and steady wins the race.