I've done it a couple of times. Strategy? Lots of coffee!

haha honestly I did one that was planned out hour by hour based on avg. wait times and travel time and all that (aka super crazy ocd day). But the last time it wasn't really planned, the weather and crowds and park hours just kept me moving along between parks and I decided to just go with it. But what I'd do is list 3 or 4 attractions (I did 5 actually) that I
must do and then a list of 4 or 5 attractions I wouldn't mind doing/seeing to fill in the extra time per park. I give myself at least 2 hours (usually more like 4) in each park to do so + 1 hour commute per park + 1 hour lunch + 1 hour dinner. I took advantage of EMH in the morning and my last park would be MK since it's usually open the latest. During my impromptu 4 day adventure I apparently did EMH AK -> bus to DHS -> DHS -> walk/boat to EPCOT -> EPCOT -> monorail to MK to close out (and judging by my pics I did all 4 before the sun even went down). But the best thing is that there are no rules! The last time I barely spent any time in DHS and just decided to after a few rides and walking around for an hour that I was good and moved on. A fun and easy way to document it (and to brag to family and friends) is to pose in each park (apparently I learned to count during the process too

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Looking at your signature I'm guessing your days are pretty packed already so I don't know if there is a "good day" for you to do it. I think the parks close a little earlier since the kids just started going back to school (not to mention
MNSSHP is starting up too), so hopefully the crowd levels would be low enough to tackle the parks much quicker; looking at the park hours I think the BEST day to 4 park it would be on Sat the 19th though, simply because you have the most hours to work with. That Monday might be tricky though with only (haha) a 12 hour window to work with.
But just give a little thought to what all you want to "accomplish" on your 4 park day and go with it. As long as it's not
too crazy of a plan you should be able to do it.