Here's what I'd do - if I got it right from you...
Buy new sand for the new tank. I like the 3" depth too. Purchase new base rock. After rinsing the sand VERY well, add it and start your aquascape with the dry base rock. I did the exact same thing and found a lot of flat pieces. Actually, those flat pieces went in first, really under the sand. Then the sand. Added the new SW
, about half full or enuf to receive your established rock from the 55g. Now, you gotta test the water with the base rock in case of ammonia from dried organic matter that will decay again when in water. If the rock is good and tests OK, add the established stuff too.
I'm thinking you can make an easy transition without cycling anything. May have to add the fish slowly. I'd leave the last few pieces of established rock in the 55 until they're all gone.
Boy, I got talkative... HTH