My impression is that with the huge capacity of the value resorts that have been added to WDW in recent years, the EMH program is not nearly the benefit that it used to be several years ago. The crowds are such that this thing is now more of a "penalty" than a "perk," especially during the busier seasons of the year (IMO).
I think a much better approach is to avoid the EMH parks.
As Disney Queen says, you can hit the morning EMH park, then hop someplace else, but I guess I don't see the advantage of doing that (with all respect to DQ). When you hop, you can't get any FastPasses for later in the day at the EMH park (because you won't be there), and when you hop someplace else, you're at a distinct disadvantage with FP there too, since you weren't able to collect any FP's at that park during the morning hours.
You could hop to Epcot only to find the FP's for Soarin' to be already gone, for example.
It seems to me like you can get as much or more done by avoiding the EMH park, and have the added benefit of not having to get up that extra hour earlier!