"Moving fast?" I'm not following you. BUT, here's a scenario or two:
1. If your kids are early risers, Rope drop park A, beat the crowds, leave the park in mid afternoon, when the crowds are the worst, and the sun is the hottest, return to the resort to enjoy that pool you re paying for (when the sun is the hottest, and the crowds are the worst, and the hop to EP or DHS for a lazy "tour" and nighttime show. When you are only a few minutes away from two parks, hopping is pretty freekin simple. Also the International Gateway is a "chill" entrance for Epcot. If I stayed anywhere besides an Epcot area resort, I don't think I'd get hoppers.
2. Epcot or DHS am EMH? BREEZE. Absolute breeze. Ep opens at 8am for emh? You leave at 7:40am, and you'll be there before rope drop. Dhs - budget 25 minutes to walk. I'd budget something like 40 minutes for the boat (with wait time included.) You might get lucky and shave 15 minutes off if you don't have to wait for a boat. BUT, along with that, getting back to your room for a mid day break is nothing.
3. For the price you're paying, it might be wise to tag team the kids a few times at night. Again, 10 minute walk to World Showcase, 25 min walk to dhs. If the kids are dead asleep one night at 8pm, one of you could slip out and for a few hours and do some solo adulting at DHS or EP for a few hours and probably not be any worse for the wear. Especially if there's a pm emh at EP or DHS - again, your travel time is NOTHING.
Disney transportation can start weighing on your vacation time over the span of days. Epcot area resorts are pretty special because you can walk to two parks pretty easily. I mean Epcot Ig is just a breeze to get to DHS is about twice as far of a walk, but unless you catch a boat at the right time when you are leaving, walking back might be faster than the boat ride.
I guess I'd suggest to start thinking about what you'd like to do, and what's right for your family. Take recommendations of course, but, you don't have to go along with recommendations if it doesn't make sense for what you want to do. I know you probably already know this. For the price you are going to pay, make the choices that are right to you after thinking them through.
My opinion is that epcot are resort + kids that wake up early = hoppers.
Also, if you are a Costco member, take a look at their WDW packages.