If you're going on one of the days expected to hit capacity, just be sure you're there earlier in the day and it won't be a problem (beyond the crowds getting around the park, of course). You don't want to not be let in the park, but if you're there in the morning you should be fine and it will help avoid stressing about what if this is THE YEAR or THE DAY that is more crowded than it has been in ages. Just don't try to park-hop or go back to your resort for a break on these days.
For these kind of days, I'd recommend a long, slow day around the park. Other than your fastpasses, you're probably best avoiding rides. Do activities like Sorcerers of the Magic Kingdom and the Pirates Adventure. Do some shopping. Relax and have leasurely meals at your adrs. Stake out spots for parades and fireworks well in advance, but have fun with it. Bring a blanket and alternate who is waiting, or send people on quests to bring seasonal treats back to whoever is in one spot. Whoever is holding the spot could also bring cards, an iPad, or a kindle loaded with books to entertain themselves. Basically, capacity days should not be thought of like other days. Even the most unpopular ride will have a wait. There are, however, a lot of great ways to spend your time, have fun with family, and not be stuck moving from one long line to another. Planning ADRs is a great start to avoid QS lines at mealtime, though do be prepared for both places to be running behind.