Hi Rachel, first off big (((HUGS)))
It sounds as though things are going really well, despite today's nap, no? If your DD is anything like my DS (and I think we have discovered that they are!) she probably shifts day sleep and night sleep quite easily and also shifts sleep from one day to the next. For example, if my son has a nice long nap, he will still go down at the same time but will wake early the next day thus making it hard to get to nap time then short nap. Or he may have a nice long nap and a nice long night only to short nap and have a short night the next day so he gets OT then a cycle starts. Have you logged how much sleep she gets in 24 hours? I know my son needs about 12.5-13, closer to 12.5 these days.
Since you are trying BTC, the best way yo get some more consistency is to make bedtime, naptime, nap length and wake time all the same time (within reason of course) every single day for a week or more (it has taken us 2+ to get anywhere close but I think we are getting there, just now) and I promise you will see changes. It has worked wonders for us in the past to recover from OT, become more consistent and to save me from a mental breakdown!
From your posts, it seems 12-12.5 might be her overall sleep needs. So if she really only does 10ish comfortably at night so she needs 2 in the day. So set a schedule around that and be super rigid. So one day she may wake at 5:30 and nap longer, like 2.5 then her next night will be short thus making her OT or her night may be long so she short naps the next so she gets OT. Am I making sense? She will get OT, she will get cranky, she may even have NWs and EWs but it has worked for me (and many others who have offered advice to me) and after all I have been through, I never would've imagined that it would get us out of the mess we were in. My son has always preferred long nights and shorter naps. He rarely naps over 1.5 hours. 2 once or twice a month. I have tried and tried to shorten his night but it makes him OT. Seems that your DD is the other way around. She likes longer naps (2 hours? and 10-10.5 nights).
Could you try
6:30 wake
nap 12:30-2:30 nap (wake after 2 hours until her nights get to 10.5 consistently)
8pm bed?
I know early bedtimes help some to get over OT but I also know that your DD is not a long night sleeper no matter what so she just wakes super early, right?This could work if you limit her nap and not get her until her wake time of 6:30am. We have been doing this, leaving my DS until 7am for the last 2 weeks and finally he is waking later. With my DS we need to just leave him, if we wi/wo at that time he gets so upset and thinks we are abandoning for the day. Sorry this is so long, but after all that you have endured I wanted to share my succes with you so you don't give up. Hang in there!