Hi there,
It sounds like your baby is BFing for comfort at night and not for hunger or need. It also sounds like she's taking in only a small portion of her BM during the day and getting most of at night, which of course, is opposite of what you want. I encourage you to get away from night feedings, at least 2 of them. Your supply should be well well established at this point, there shouldn't be any problems if you discontinue night feeds at this point. For example, my DD has been sleeping 12 hours, with no feedings, since 2 months, and I am still BFing her during the day regularly, and she is now almost 12 months. I never lost supply as a result of not feeding at night.
What about offering milk before solids during the day? That would make sure that a) baby gets more milk before taking solids in, and b) keep you from BFing her to sleep before nap time.
Here's what our routine looked like at 9 months, of course all babes are different...
8am - wake and BF
9am - breakfast
10:30am - nap
12pm - BF
1pm - lunch
3pm - nap
4:30pm - BF
6pm - dinner
8pm - BF and bed
Best of luck!