How do you think she would react if, instead of sitting outside listening to her sing, you told her not to sing and to go to sleep?
I can remember doing this with DS, I was outside and said something like "Be quiet. It's sleepy time, Go to sleep." My tone/attitude was pretty much and "I'm in charge, I know what's good for you, it IS sleep time, you need to sleep" instructional in the same way I might tell him he is not allowed to go near a hot oven or pick up the glass bottles in the supermarket or that we have to brush his teeth - non-negotiable tone. Do you know what I mean?
I also used to (when putting him down more than once I was out of the room) say to him things like "You may not sing now, go straight to sleep and you can sing all night in dream land, all your friends are there waiting for you, ready to sing with you". I suppose my approach was more like if he was singing top of his voice in the middle of the night and it was disturbing other people, just because it's only 7pm ish doesn't make singing acceptable.
I'm mentioning this because it seems you've tried a lot of tweaking without getting anywhere and it's perhaps not just routine which is impacting.
So, WRT routine, couple of thoughts (although like I said previously, think I'm more lost than you!)
- when was the last time you did not cap the nap, how long was it and did it make any difference?
and the opposite thought
- what if you capped her nap at 30 mins one day, not as a routine change but as a one-off? YK like one of those days when the nap is unavoidably disturbed somehow and you know you have to just wing it that day and get back on track the next?