Will go back and read, but EMH only covers guests at DL Hotel and Grand Californian, no? If so, even if every single guest wanted to get a BG at EMH opening, there would probably be still be regular BGs available to offsite guests? If so, I could see (I hope) allowing EMH guests to get a BG first, since this might help split the attendance to on/off property days. On-property, just go to EMH and don't worry about it, and stay away from the non-EMH days, thus leaving more BGs open for local and offsite guests.
Note: I am staying onsite in April, so I may have some bias here... but one distinction with DL and WDW is that WDW has so many onsite guests (possibly 100k in 30k rooms, acc to Google) that having morning EMH would shut out all offsite guests *and* a large number of onsite guests. So the fairness aspect of EMH may be different here.
Note2: We got up "at the buttcrack of dawn" as my friend called it, to ride RotR 2x at WDW. 5:30am with a double stroller. It was worth it.