What are the optimal simmering times for each stage of a traditional phở?
This is not the answer you are directly looking for, but may be the trick

Some local Phở brewers soak the onion skins in alcohol (rice cooking wine) to extract a stock flavouring (I suspect this is Quercetin?). The resulting dark liquor is added to the broth when the meat is added

This certainly kicks up the broth flavour, a bit like MSG does in Chinese cooking (sort of)

Worth a try...

I don't think there is a magic order or timing to making Phở, as long as the flavours are extracted, and not destroyed, it comes out OK