This is what I did when I transferred my 30 to my 75, but I still have the 30 up and running.
I use a 5 stage RODI system to make my water, and I can only make 30gal at a time, so I made 30gal of water, put it in the 75 with new liverock (and sand, put the sand in first) let it sit by itself, make another 30gal, and when I did my water change on the 30, I put the old water straight into the 75 to sort of speed up the cycling process. Once I had it filled up and running, I let it sit by itself for about a week, doing another water change and putting some water from the 30gal into it. Cycling didn't take long at all, then I very slowly started moving the livestock over. About a fish a week. Coral was all at once when my new lights came in. But since you're moving into a 180, you could just add all your fish from your 40 all at once.
This was just my method, good luck and ask any questions if you're still confused! Best thing is to just take it slow and think before you do something!