Disney resort buses drop off near the MK front gate bypassing TTC.
Assuming the 24th is the actual day of the Princess 1/2, I'd probably avoid both MK and Epcot. Epcot has the start and finish but the course also goes up to MK. I did the ChEar squad in 2017. Spectators are allowed into MK before it opens for the race. To help get us back to Epcot for the finish, they loaded us onto the monorail from both the exit and entrance at TTC. Traffic was heavy on World drive as the runners are running beside it, which means heavy patrol car coverage for the runners' safety. This impacts buses getting to/from MK. I just checked a photo of my DIL as she came through the castle and it's time-stamped 6:13 am. She started in one of the later groups and there was still MK course to be completed after the castle. I'm guessing MK was cleared of spectators by 8:00 am or, shortly thereafter, but I'm not sure when World Drive was cleared. Epcot opened while there were still runners on the course.
My Runner and I had park hopper tickets, so we went into Epcot first. Then early afternoon, she wanted to take photos at MK with all her medals. But then she headed back to the resort to rest since she'd been up 3 days in a row at 3:00 AM and ran the 5k, 10k and half. So I'm not sure the runners make much of an impact on crowd levels as the day wears on.
Any day other than the 1/2 day, everything is done long before park openings.