Hello Hun,
I think it's important that you as her Mum have faith in what YOU think she needs too. I know how blinkered you can get when you're in the thick of it, so from what you've said here's what you know:
She doesn't take kindly to being put in her cot unless she is ready.
She doesn't show sleepy signs until you wind her down.
She likes a long first nap and any second nap would be a cat nap.
Going with the above here is what I would suggest:
Wake her up at 5 am (I know! it's harsh but it's short term)
Give her a good long low key wind down from around 4 hrs 15 mins so 9.15 am to try and achieve her nap by 9.45/10.00
Put her in her cot once wound down and sit with her maybe one hand on shushing (if this is necessary? Sorry I know you said she SS alone for her nap but don't know if that is in her cot or not?)
Leave her to sleep until she wakes, hopefully at least 11.15/11.30 (cap at 2 hrs if she happens to sleep longer than usual though)
Try for a cat nap in the cot around 3.00 pm (winding down at least half an hour before as per morning) again staying with her if necessary using only a sleepy phrase and no eye contact. Keep her there for around 20 to 30 mins then abandon if it's a no go.
If cat nap is a wash out try and keep the A time to BT low key.
BT 6.00 pm. Same as earlier in the day, long WD then staying with her with a view to using gradual withdrawal for all sleeps once into her routine.
I think there is an element of ST needed Hun. She sounds to me like she needs routine to set her body clock, especially if she has no sleepy cues.
I would stick with this for several days (at least a week) if you possible can and see where you're at. If it works hopefully she will get over the OT and she will shift the routine herself and start to consistently wake later. In an ideal world eh

Ultimately you might look at shortening the first nap and pushing it out later, and the cat nap being around 20 mins until she is older and can pull one long nap.
At least with the early morning and full commitment you should get plenty of you time in the evening.
Let me know what you think.x.