If it helps, I find that when we go through phases of this, it doesn't last TOOO long. But does come in phases - if DS is going to wake early because he has pooped, then he will do so every single day for about 2 weeks until it just passes. We also get the poops that happen as he is on his way to bed (I'm convinced he squeezes them out on purpose to delay bedtime), and that will last for about 2 weeks, and right now we are getting a nap-interrupting poop...he falls asleep, and wakes 10 minutes later with a poop, and I have to change him and put him back down. Does not matter if I wait 20 minutes for his nap, he holds the poop in until he's been asleep.
I have thought that it might be phases where he is a bit backed up and it is the relaxation of drifting to sleep that means he is relaxed enough to poop, but haven't figured out what the 6am one could be!