10-12 feeds at this age IS normal. I know it feels like you're feeding ALL the time and looking at your schedule above, like the pp said, looks like classic growth spurt to me too.
You mention a big nap in the afternoon. How "big" is that nap.
How can I get her to take a full feed in one go so that she can manage at least 2.5-3 hours between feeds?
Really you just need to keep doing what you're doing. It's just kind of an endless circle of trying to encouraging good feeds, letting them sleep when sleepy, and starting again. I'm sure you've tried this but I used to do a diaper change when my lo would fall asleep nursing and then finish up the feed. Sometimes it worked...sometimes not.
Also, I know I did anything and everything to get some good naps so we could get good feeds. Sometimes some APing, like a swing, letting them sleep in a carrier, whatever works really. My focus at this age was getting good feeds.
Regarding her sleep, have you tried sssh/pat? You may want to check out the sleep boards for some ideas on helping her to sleep.
You really are doing well. Hang in there! It's early days yet. She'll get there.