Pat/shh and pu/pd are methods to teaching independent sleep. You say your lo is falling asleep in her crib - are you doing pat/shh and/or pu/pd during the initial falling asleep as well?
I have to say that when we've used pat/shh with DD#2, I always set a limit on how long we are going to do it. If she's not showing tired signs within 20min or so, then I get her up and we continue on with A time if needed.
Pat/shh and pu/pd are used to "extend" naps for a baby who is waking early because they don't know how to self soothe through the sleep cycle transitions. It is not going to work on a baby who has gotten a good nap, and is no longer tired (since the goal of pat/shh and pu/pd is to help a baby go to sleep), and it is not going to work on a baby who has another need that is not met that is keeping them from sleeping such as hunger.
Has your lo been sleeping through the night prior to starting EASY? Is she hungry at the 5:30am wake up?
EASY is not a strict schedule that you have to keep - it is a routine or an order on how activities should occur, so if there is some A time before the next E, and your baby is happy and content and well rested, then that is perfectly ok! If a feeding needs to be earlier or a nap earlier than normal because that is the type of cues she is showing you, then you follow her cues. So if she woke early from one nap, then you can always feed her at the appointed time, or whenever she shows hunger signals, and then a very short A time and go ahead and try for another nap. Sometimes EASY looks more like EASAE, and that's ok, because they older a baby gets, the more their routine is going to look like this naturally because they don't nap as long.
A times for a 4mo are typically right at 2hrs, but if your baby is 4.5mo or more, it may be that she needs more A time in order to take a good nap. Your routine looks pretty good based on a typical 4mo old.
Just some thoughts! Hope that helps!