Doing a dry run ahead of time is a great idea. It will really help things go more smoothly that early in the morning!
You know your family best and how easy/hard it will be to get them up and going for your MM. I tend to agree with you that Thursday might be better since your family will have more energy and momentum going. (Also, if something goes wrong and you can't get everyone up in time or if the parking plan goes awry, you'll still have Saturday in your back pocket.) M&F does open 90 minutes before MM (all parking info here:
https://disneyland.disney.go.com/guest-services/parking/), but there will be a line of cars waiting even before 6:30 am. How long a line? It shouldn't be super long, but there will be cars already waiting. Ask in a new thread closer to your dates once the Spring Break crowds really get going.