THe shrooms and xenia will survive a moderate cycle, easy. The problem is you can't move the big tank without totally breaking it down, and any time there's a breakdown, the tank and/or sump has to cycle, which will mostly involve the bacteria re-layering in the sandbed.---it'll be mild. I've had even bubble coral survive a full-blown cycle. But any fish are vulnerable to the ammonia. Corals will just close up.
Here's what you do, in a nutshell: break down everything, use the waste water to wash the sand til it's pretty clean and concentrate on the tank. Let the sump fuge set up gradually once you've got the tank functioning: just start adding a little rock, then a little sand to the new fuge, and you can go ahead and add cheatomorpha algae and light it 24/7.
Start everything in the tank with new salt water, but old sand, old rock. It's going to be about 5 days til there's a mild spike. Stand by with Amquel if it gets too bad, but it shouldn't. And treat it very gently re temperature, re lights. Just view it as starting all over, but it should go quickly. If you can keep your fish in a 32 gallon Brute trashcan with a good pump, and heater, they should be fine: no cycle for them, just a lot of filter changing and salinity testing: test everything. Scary re the corals, but if my bit of bubble and some mushrooms could survive January temperatures, new water, a 4 week cycle, and all, your corals can likely make it. If you're worried about the hammer and frog, put them in the dark bottom of your 32 g trash can. That water will be under-used throughout and should stay pretty good, with just a few fish. And at the end of it, you'll have a spare trashcan you can use for packing and have for emergencies.
Does this make sense? Tank #1 priority, fuge to take life from the tank once you get the tank going strong, corals in tank or in can, fish in can, watch the ammonia like a hawk, in the can!