Did you pick up the materials that morning or did you go get them on Wednesday.If you are running in the adult races, I would aim for getting Thursday. That way you have the most amount of time from finishing your race, breakfast at the food court, back to your room for a shower/change, and then back out to WWOS for the kids' race. I did that this year and we were at WWOS easily an hour before DS had his 100m dash.
DS has only done the Mickey Mile (twice), and it hasn't seemed overly crowded except for at the start b/c parents are allowed to run with kids (they do NOT get medals though).
Do the day that works for you.