Hmmm I've been thinking about that a lot too. Here's my plan:
I am going to move all my rock, corals and fish over to rubbermaid tubs, with new water in the tubs. I'm going to drain the old tank, saving the old water in another rubbermaid tub. Move the 55 out of the way, and move the 240 into its place. It would be much easier if the 240 was going in a different location! I'm using the 55 as a sump, and it needs to be placed through the top of the 240 stand, so I'll have to empty and clean the 55 completely, silicone in the baffles, and get the sump put together immediately. That should take a day for the silicone to cure.
The next day: Now this is my chance to get rid of that damn crushed coral I started with! Fill the 240 with aragonite, add the old water to the 240, and fill it up with as much new water is needed. Then move all my rock, coral, and fish into the 240. HOPEFULLY a cycle won't start! I don't really see why it would, except maybe for having new sand and so much new water. I am planning on getting a lot more live rock, but I will probably have to add new rock slowly over time to avoid having another cycle.
I figure my corals and fish will be fine in a rubbermaid tub for two days without any lights and only a heater and powerhead. So if I can get this switch over done in a couple days, I think that'll be okay. It all depends on how quickly I can turn my 55 into a sump, since that needs to be placed into the stand before I can put anything into the 240. In the meantime, the livestock will just have to chill in a tub.