As a Disney coaster enthusiast I love the idea of this challenge. Here's what my way-too-detailed strategy would be:
1) Start at Animal Kingdom, it has the earliest opening time at 7:30 with the early entry hours, and only one coaster you'll need to check off your list: Expedition Everest. Getting there that early PLUS the single rider option should make it where your family can check it off in no time and move on. Overestimating a little probably but I'll say you'll be done at AK before 9:00.
2) Hit Magic Kingdom second. Bussing from AK to MK will probably be your longest travel period, but let's say you'll be at MK around 10:00. Ideally, you could get a decently early VQ spot for Tiana's, use a tier one LLMP at either Big Thunder or Space Mountain, tier two LLMP for the Barnstormer, and LLSP either Tron or Seven Dwarves. If the stars align for this, you'd only have to standby for two attractions. Eat lunch among the madness here somewhere. As for scheduling out those VQs and LLs, my strat would be:
- Use your tier one LLMP for Space Mountain rather than Big Thunder, as VQ return times aren't an exact science and therefore it'd be hard to schedule Tiana and Big Thunder return times close to each other.
- Use your LLSP for Tron rather than Seven Dwarves. Tron is newer, so its standby will likely be longer. You only get two LLSP a day, and I'd say to save the second one for Cosmic Rewind.
- Try to schedule a Space Mountain LLMP and Tron LLSP within the same hour, or as close as you can. Clear Tomorrowland in one fell swoop.
- After using your Tiana VQ, go on and get the standby for Big Thunder out of the way if you can. Same idea as above, clear Frontierland in one fell swoop.
3) As soon as you use your LLMPs at MK, check to see if you can find LLMP spots available at the Hollywood Studios coasters. Slinky Dog isn't super likely but MIGHT have a spot if someone altered their selections or something. But I'd say a spot on Rock n' Roller Coaster is more possible.
4) MK is by far the heaviest load in terms of coasters, but if all goes accordingly with VQs and Lightning Lanes let's say you finish there by perhaps 4:00. Hit Epcot third, take the monorail over there, arrival by 5:00. Hit Cosmic Rewind using your second LLSP, ideally between 5:00 and 6:00, eat something for dinner either before or after this ride. While you're in Epcot, see if there's a spot in the VQ to ride it again, but no guarantees here. I don't see any good way to guarantee two rides on Cosmic Rewind in a scenario where you're trying to hit every coaster on property AND a different VQ attraction.
5) Last stop of the day is Hollywood Studios. Exit Epcot in the back at International Gateway and hop on the boat to get to Hollywood Studios, you certainly deserve to get off your feet by this point. Or walk it if you
really want. Either way, ideally you'll be in Hollywood Studios around 7:00. Depending on wait times and whether you could grab a late LLMP at either coaster here, check them off in whatever order makes sense.
I think that in general this challenge will be reliant on luck and availability, but I don't think it's impossible if you use your resources well! I hope you'll report back on how it goes if y'all do make an attempt!