I started with a plan of looking for all 12 at once and would switch to smaller groups if necessary. I was able to find everything for all 12 without breaking up, including 7dwarves. The earlier of my 2 MK days, I had at least 5 choices of times for 7dwarves, but not times I particularly liked and the later MK day I had lots of availability all day, still no breaking up. I did do that MK day only at midnight, but then went to bed and did all the rest (all 12, no problems at all) at 2 pm the next day. I have since played around with a couple of times and always got plenty of ride and time choices still for the entire group at day 42 and 38 and 35 so far.
If you're a night owl anyway, I think you'll easily get all you like at midnight. If that's tough, I'd really think you can easily wait until the next morning or afternoon. I also watched a youtube walk through of the process so I'd know what the screens looked like beforehand, so I'd not be seeing it the first time when I'm tired and impatient