Watch for park closing times and special events. You probably won't be able to book dinner too late in September - MK often closes in September around 6:00 pm.
I'd encourage a late lunch at CRT, get out of the heat and crowds around 1:00 or 2:00, but be back out in time for the parade.
Only dinner at LTT has characters, and your "late" dinner choice may be 4:30.