Moving at night is easier - that's what we were PLANNING to do - but the way it worked out, we did it first thing in the morning. We had 100+ chickens to move, and had as many large dog crates as would fit in a Uhaul cargo van (6??) - the cargo van was perfect-- and we needed it anyway to move the goats (200lb goats, not going in my car!). My last coop could be kept pretty dark, so my strategy was go after the super easy birds first, then the flighty ones (so they wouldn't be bouncing around all over), then the in-betweeners. I think it took us 2 trips in the van - 7 or 8 to a crate.
This is what made a HUGE difference. We put a 1/4" rubber mat (usually sold in a roll, by the foot, at the farm supply stores, 30" wide, 1/4" thick, very easy to cut to size) on the bottom of each crate. Everyone rode SUPER well on the hilly, non-stop curvy drive from the old house to the new. The one crate I forgot to cut a mat for --- there was a LOT of scrambling- doesn't matter how much bedding you put in a crate, what they need is traction. I felt bad about that!! The mats made ALL the difference - just a regular box cutter will cut them, and the 30" width worked well in the dog crates.
We carried the WHOLE CRATE with birds inside to the new coop, closed the door, then opened the crate and let them out. In our case it sucked because it's a steep hill to get down to the coop, but there was NO WAY I was opening a crate door in the driveway. Not a chance. Once the crate was in the coop and we got them to walk out--- they pretty much just walked right on out the pop door to their new gigantic run and got down to the business of being chickens.
I *did* have issues the first couple nights getting my silly hens in - there was a log jam- the ones too scared to really go in caused a big traffic jam, but I didn't have to do anything beyond clearing the chicken snaggle.