I always do wash halfway through our week. That’s the same time as we plan a resort-based day. It is a sleep-in for most of my family, and I’m usually awake earliest. Knowing this, I get everything together before bed in the collapsible laundry bin that we bring along, along with detergent pods and dryer sheets. When I’m up to go get my coffee, I go by the laundry first - I’ve never had a problem getting a machine in the morning at AK, Pop, or Poly - and I pop my stuff in. Note that you’ll need a credit or debit card to activate the machines. I go get my coffee and have a stroll around my resort. By the time I’m done, the wash is ready to move to the dryer. Typically, my family is also beginning to awaken, so I’m able to bring back the hang-dry items after making the switch. An hour later, I go get the stuff from the dryer. I’ve also done this pattern on a park day (albeit not a RD day) and get the stuff in the dryer while everyone is getting ready; when they’re done, so is the wash.
I also tend to do this on depart day - or if necessary, the day before depart. It’s really nice getting home with only clean laundry.
Here is a blog post I wrote not too long ago about laundry at WDW: