That sounds exhausting and frustrating!
As it's been going on for months it appears not to be related to the time of his feeds/meals so I wouldn't think there is anything you can really do! The only things I can think you might consider are:
- W2S before the 4.30 poo, so maybe 3.30am to see if you can start a new sleep cycle so his body doesn't come up the the light sleep or wake up at 4.30 but instead he wakes a little later for the poo. This may make things worse for a while because initially the WU won't be as late as 7am and he'll likely still need to go back to sleep but this then impacts the rest of the days routine as you'd still need to get him up at 7am to manage his day naps. If it did move the poo time you may be able to do it again at a later time to achieve the 7am WU and poo. It's certainly not a definite but you might want to try?
- gentle tummy massage (clockwise) and leg cycling in the afternoon to see if it makes a difference to his poo time.
- sorry the other thing I thought of was to move his whole day on, like a clock change but now I realize this isn't possible as naps need to be at those times around the school run.