Berluddy hell, she goes to bed late!!
Our evenings are sacrosanct - M goes down from 7 at night until 7.30 in the morning and although I love the bones of him, that fact that our evenings are our own and baby-free makes it all a LOT easier. Plus, your little one is now swapping day for night - 7 hours of day time naps is too much for a baby of that age, and it just shows that she is not getting the night time sleep she needs.
Totally agree with TRD - it's time for a bed time routine. I know you say you've tried this, but I would really recommend persevering with it. It will take
at least 3 consecutive nights, of absolutely the same routine for her to start to get the idea, but could take a lot more than that. You will need to be absolutely consistent in what you do, so that she gets all the signals that it's time for bed.
For instance, at 6.30 I take M up for his bath. After his bath, I put a new nappy on, massage him (with the same oil each night, so he now associates that scent with bed time), dress him and then feed him. Into bed at 7. OK, that might be too early for you, so try a little bit later.
The first few nights you will probably either have to soothe her by the cot, or leave the room and continually go back in to soothe (better, since if you stay and soothe by the cot, she will keeping fussing to keep you there). It will be hard work and it won't happen overnight, but short-term 'pain'; long-term gain. Don't pick her up, and definitely do not take her out of her/your room. It was hard work for us when we started it at 6 weeks of age, but my God it's paid off. He's a happy, content baby when he goes to bed now, and goes straight off to sleep.
It really does sound like she's simply not getting enough sleep for a baby of her age. Every baby is obviously different, but most babies around that age need c. 3 hours of day-time naps and 12 hours of night-time sleep. Give or take.
And as TDR says, depriving her of sleep (either day or night) will only impact on her overall sleep. I mantra I have lived by is that 'sleep begets sleep'. Naff, I know, but the better sleep they get in the day (and by that I mean sufficient sleep, not taking over their night time sleep b/c they're not getting enough then), the better they will sleep at night.