I visit about 3-4 times a year (visiting my CM daughter). I always travel at busy times - Spring Break, Halloween, Holidays. I rarely make ADR's. Instead, I book same day, sometimes day before. My last trip was busy Thanksgiving Weekend 2022. Searching same-day dinner (beginning at 2pm) and looking for a party of 4 around 6pm, I found the following available on Friday (Black Friday) and Sat nights:
CRT
BOG
California Grill
Citrico's
Storybook Dining at Artist Point
Ohana
Citrico's
Tons of other choices as well
I also looked on Saturday for a Sunday morning breakfast or brunch, and found a reservation for Topolino's breakfast at 11 a.m., which I booked.
Sci Fi had availability every day I looked, for lunch and dinner.
Party of 6 would be more difficult, no doubt, but I bet you'd still have some good choices same-day.