Hollywood studios, in particular, is not noticeably less crowded on non-AM EMH days. They have so few attractions that are open for the extra hour that it's definitely not worth getting up the extra hour earlier for. Get there 40-45 minutes before opening on a normal day, and they'll start letting you in 15 minutes or so early. You'll be fine.
With little ones, MK is definitely worth getting up early for AM EMH, as almost all the rides they would want to do are open. I would even say for the older ones as well -- they could get multiple rides on SM in before it gets crowded. But again, it's no big deal if you don't. What smaller crowds may exist during that first hour of EMH, are quickly dwarfed by the increased crowds added to their number beginning at regular park opening as the vast majority of the people staying off site, or who otherwise don't pay attention to EMH. start to arrive. So, on an AM EMH day: 8-9, somewhat less crowded; 9-3, noticeably more crowded than a non-emh day.
Said another way -- the first hour of a non AM EMH park generally feels about like the first hour of an AM EMH park -- though some parks may be somewhat less crowded. Most of the planning web sites would say that the increased crowds later in the day make it ultimately not worth the extra hour of somewhat diminished crowds, unless you have a park hopper and can get to another park.
So get your sleep!