The MK is tough on party days because the last FP+ window closes at 6:30 (and the park closes so early). I was able to get POTC once on a party night, but only at overlapping times. We lucked out with Talking Mickey once on a non-party afternoon after we'd spend the morning at DHS, but again, only with overlapping times. The problem I've run into is that by mid-afternoon, anything that might still have FP+ availability probably doesn't have a long SB line. Like I know we were able to pull FP+s for the Flying Carpets for 15 minutes in the future...but the SB line was only 15 minutes. Same with VotLM. Jungle Cruise and Buzz both seem to have pretty open availability and long SB lines so those are probably good bets. The only times I saw "mountain" availability was for late in the evening when pulling early afternoon, which never worked for our plans.
DHS: Star Tours, Great Movie Ride, BatB, and Fantasmic.
AK: Lion King and Nemo are the only ones I remember seeing. No rides.
Epcot: Never tried for a 4th.