She wakes early even when she is "on track" (6am)
It's one of those things you either live with the EW or you live with later BT - that is, if your LO does less than a 12hr night or if your LO is going through a routine transition where the night is shorter than they 'can' do but is necessarily short because they can't totally drop or cap a nap.
I would have been happy (ish) with 6am. Mine was always a 5am waker, to me that is the middle of the night.
Like yours mine has a very strong body clock which wakes him at a set time regardless of him being tired or what time BT was, however I did eventually work out how to break his body clock and set a new one. The daylight saving hours time switch suggests moving the whole routine by 15 mins until the hour is achieved. I found this just meant mine had 15 (then 30 then 45 then 1hr) less sleep per night, adding up to a huge sleep loss and a very cranky boy. What worked was rapid movement of the times and taking him beyond the hour change (my plan was up to 2hrs but I think he shifted his body clock at 1.5hrs), the sleep loss happened faster over fewer days so overall it was less and his morning WU did shift. Once the morning WU time has shifted and a new habitual WU time is established the BT can be brought a little earlier again - but not too early, they can only sleep as long as they can sleep, yk?
I would continue as you are and see where things settle. Then if WU is still earlier than you want you can consider trying to change it (and accepting later BT if necessary). Sorry, probably not what you want to hear. I would have also loved a 12 hr night, as it is mine could only do 10.5 or 11hr max, that's just who he was. It wasn't until he totally dropped his nap altogether and settled into a no nap routine that he was finally able to get a 12hr night - ah what bliss! He was 31 months then.