Hugs Franziska! 4:30 is rough! You must be exhausted. I bet you tried to resettle her? How?
TBH, with an EW of 4:30, I would apop or support however until 6:00, then expose her to light. Totally use your judgment with these, but a 10 min CN around 9:00 may help. Then put her down for a proper nap around 11:00. The goal is to get her to 11:00/11:30 consistently without accumulating more OT.
I know it must be extremely difficult to handle apop CN's with another child.. I can't imagine! however, it (morning or evening CN) may be your saving grace during this transition. If not at all possible, it's ok. If there are opportunities to do so, it may help.
I'm sorry to hear that the EBT isn't working completely for her. It may be worth a couple more days to see if she can tack on sleep in the morning. I agree with what Nicole said, such a tricky stage! Independent sleep is when you can put her down awake, leave, she falls asleep, and does not need you to return for any support. If this isn't the case, then we can also work toward giving her opportunities to self settle.
Keep us posted!