I wouldn't move the sand out of the tank before the fish get moved out. Mixing up that sand will do some nasty stuff to the water that they're left with. If I was going to add rock to a system and I didn't want to see a cycle I'd use dry base rock rather than uncured rock as I'd be very worried that the uncured rock would start a cycle.
1. Fill new tank with ~2" dead sand. (I only want a 2"-3" sand bed)
1a. Move fish & corals to a temporary holding tank with water from the 55.
1b. Move all water that I want to re-use out of the tank into a rubbermaid, etc.
1c. Rinse the sand in the remaining water in the 55.
2. Place sand from 55 on top of new, dead sand.
3. Transfer 70# LR
from 55 to 120 while keeping attached corals in the holding tank.
4. Add about 20# more base rock (even better for controlling costs).
5. Add 30 gal
6. Add SW
that was saved from the 55 into 120.
7. Transfer corals and fish.
8. Dump remaining water from 55.
9. Add new SW
to fill and complete.
10. Will add more rock as weeks progress.
There are my thoughts... Good luck!